Math Problem Statement

Solve the quadratic equation to find the values of x.

Solution

The image you've uploaded contains a mathematical problem that asks to find the value of xx when the given expression is simplified. The expression provided is:

2x2+3x2=3x2x^2 + 3x - 2 = 3x

Let's solve this step by step.

Step 1: Simplify the equation

First, subtract 3x3x from both sides to move all the terms to one side:

2x2+3x3x2=02x^2 + 3x - 3x - 2 = 0

This simplifies to:

2x22=02x^2 - 2 = 0

Step 2: Factor the equation

The equation can be further simplified by factoring out the common term:

2(x21)=02(x^2 - 1) = 0

This can be factored further:

2(x1)(x+1)=02(x - 1)(x + 1) = 0

Step 3: Solve for xx

Now, set each factor equal to zero:

x1=0orx+1=0x - 1 = 0 \quad \text{or} \quad x + 1 = 0

So, the solutions are:

x=1orx=1x = 1 \quad \text{or} \quad x = -1

Final Answer

The value of xx can be either 11 or 1-1.


Would you like more details on the steps, or do you have any questions?

Further Exploration:

  1. How would you verify the solutions by substituting back into the original equation?
  2. Can you solve a similar equation where the quadratic term has a different coefficient?
  3. What happens if the constant term was different? How would that affect the solution?
  4. What if the equation was not factorable by simple methods? What technique would you use?
  5. Can you explain how the discriminant of a quadratic equation determines the number of solutions?

Tip:

When factoring quadratic equations, always check if the quadratic can be simplified first, as it can save you from unnecessary complexity.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Factoring

Formulas

Quadratic equation: ax^2 + bx + c = 0

Theorems

Zero Product Property

Suitable Grade Level

Grades 9-10