four x squared minus two hundred twenty five equals zero

To solve the equation \(4x^2 - 225 = 0\), we can follow these steps:

1. **Isolate the quadratic term:**
\[ 4x^2 - 225 = 0 \]

2. **Add 225 to both sides:**
\[ 4x^2 = 225 \]

3. **Divide both sides by 4:**
\[ x^2 = \frac{225}{4} \]
\[ x^2 = 56.25 \]

4. **Take the square root of both sides:**
\[ x = \pm \sqrt{56.25} \]

5. **Simplify the square root:**
\[ x = \pm 7.5 \]

Therefore, the solutions to the equation \(4x^2 - 225 = 0\) are:
\[ x = 7.5 \]
\[ x = -7.5 \]

Would you like more details on any step or have any other questions?

Here are some related questions:

1. How do you solve a quadratic equation using factoring?
2. What is the quadratic formula and how is it used?
3. How do you complete the square to solve a quadratic equation?
4. What are the properties of quadratic equations?
5. How can you determine the number of real roots of a quadratic equation?
6. What is the discriminant and how is it used in solving quadratic equations?
7. How do you graph a quadratic equation?
8. How do you solve quadratic equations using graphing?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Learn how to solve the quadratic equation 4x^2 - 225 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic equation formula and solving quadratic equations by taking the square root. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation