# Photomath Is WRONG! Completing the Square

TLDRIn this video, the presenter challenges the accuracy of Photomath, a popular math-solving app, by demonstrating an error in its solution for a quadratic equation. The presenter shows that Photomath incorrectly states 'no real numbers' as the solution, when in fact, the correct answer involves imaginary numbers. The video provides a step-by-step guide on how to solve the equation correctly using the method of completing the square, ultimately revealing the solution to be x = -1 ± i√2, proving Photomath's initial response to be incorrect.

### Takeaways

- 🔍 The video addresses an issue with Photomath's answer for a math problem, suggesting it's incorrect.
- 📱 Photomath initially provides an answer involving imaginary numbers, which the presenter argues is not suitable for real number solutions.
- 📚 The presenter advocates for checking beyond the first answer provided by Photomath, as the correct answer is further down.
- 📐 The problem at hand involves completing the square, a method for solving quadratic equations.
- 🔢 The equation presented is x^2 + 2x + 3 = 0, which is divisible by three, simplifying to x^2.
- ➗ The presenter moves the constant term to the other side of the equation to prepare for completing the square.
- 🔄 Completing the square involves taking the coefficient of the x term, dividing it by 2, and then squaring it.
- 🔵 The process results in a binomial squared, (x + 1)^2, which allows for taking the square root of both sides.
- 🚫 The square root of a negative number is not a real number, which contradicts Photomath's initial answer.
- 🔄 The final solution involves isolating x and considering both the positive and negative square roots, leading to the correct answer of x = -1 ± √2.

### Q & A

### What issue is the speaker addressing with Photomath?

-The speaker is addressing an issue where Photomath provides an incorrect initial answer involving imaginary numbers instead of real numbers for a math problem.

### What method does the speaker suggest to solve the given equation?

-The speaker suggests solving the equation by completing the square, which is a method for solving quadratic equations.

### Why does the speaker say Photomath's initial answer is wrong?

-The speaker says Photomath's initial answer is wrong because it suggests there are no real number solutions when in fact there are real solutions that can be found by completing the square.

### What is the significance of the 'weird symbol' mentioned in the transcript?

-The 'weird symbol' refers to the imaginary unit 'i', which is used to represent the square root of -1. The speaker points out that this symbol indicates imaginary numbers, which are not what the problem is asking for.

### How does the speaker simplify the equation before completing the square?

-The speaker simplifies the equation by dividing all terms by 3, which results in x^2 + 2x = -3.

### What is the purpose of moving the constant term to the other side of the equation?

-Moving the constant term to the other side of the equation is done to prepare for completing the square, which allows the equation to be expressed as a perfect square trinomial.

### How does the speaker determine the value to add inside the square during the completing the square process?

-The speaker determines the value to add inside the square by taking half of the coefficient of the x term (which is 2), squaring it (1^2 = 1), and then adding this value to both sides of the equation.

### What is the final form of the equation after completing the square?

-After completing the square, the equation is in the form (x + 1)^2 = -2.

### Why does the speaker mention taking the square root of both sides of the equation?

-The speaker mentions taking the square root of both sides to solve for x, which results in x + 1 = ±√(-2), leading to the final solution involving real numbers and the square root of 2.

### What is the final answer to the equation according to the speaker?

-The final answer to the equation, according to the speaker, is x = -1 ± √2, which contradicts Photomath's initial suggestion of no real number solutions.

### Outlines

### 📚 Photomath's Incorrect Answer and Correcting It

The speaker begins by questioning the accuracy of Photomath, a popular app for solving mathematical problems, when it provides an answer indicating 'no real numbers' exist for a given equation. They express concern that many users might hastily accept the first answer without verifying its correctness. To address this, the speaker demonstrates a step-by-step method to solve the equation correctly using the technique of completing the square. They highlight that Photomath's initial response is misleading and that the correct approach involves recognizing the presence of imaginary numbers. The speaker simplifies the equation by dividing all terms by three and then rearranges the equation to isolate the constant term. They proceed to complete the square by adding and subtracting the square of half the coefficient of the x term, which transforms the equation into a form that allows taking the square root of both sides. The final solution, contrary to Photomath's, reveals that the equation has solutions involving imaginary numbers, specifically \( x = -1 \pm i\sqrt{2} \).

### Mindmap

### Keywords

### 💡Photomath

### 💡Completing the Square

### 💡Real Numbers

### 💡Imaginary Numbers

### 💡Quadratic Equation

### 💡Binomial Squared

### 💡Coefficient

### 💡Square Root

### 💡Negative

### 💡Plus or Minus

### Highlights

Photomath incorrectly suggests there are no real number solutions for a given equation.

The correct answer is actually available in Photomath, but it's not the first one displayed.

The equation involves completing the square, a method not immediately suggested by Photomath.

All terms in the equation are divisible by three.

The equation simplifies to x squared plus 2x after dividing by three.

The constant term is moved to the other side to facilitate completing the square.

The b term's coefficient is divided by 2 and then squared to complete the square.

The equation is transformed into a binomial squared plus a constant.

The binomial is expressed as (x + 1) squared equals negative 2.

Taking the square root of both sides leads to x plus 1 equals plus or minus the square root of 2.

The negative sign is factored out to simplify the equation.

The final solution is x equals negative 1 plus or minus the square root of 2.

Photomath's initial response of 'no real numbers' is incorrect; the correct solution involves real numbers.

The presenter demonstrates the correct method of solving the equation step by step.

The importance of checking the first answer provided by Photomath is emphasized.

The video serves as a tutorial on completing the square, a method not immediately suggested by Photomath.

The presenter corrects a mistake in the process and reiterates the correct plus or minus sign.