(x+5)(x-5)=-7

2 min read Jun 17, 2024
(x+5)(x-5)=-7

Solving the Quadratic Equation: (x+5)(x-5) = -7

This article will guide you through the steps to solve the quadratic equation (x+5)(x-5) = -7.

1. Expand the Left Side

First, we expand the left side of the equation using the difference of squares pattern: (a + b)(a - b) = a² - b²

Applying this to our equation, we get: x² - 25 = -7

2. Move Constant Term to the Left Side

Next, we move the constant term (-7) to the left side of the equation: x² - 25 + 7 = 0

3. Simplify the Equation

Simplifying the equation, we get: x² - 18 = 0

4. Solve for x

Now we have a simple quadratic equation. To solve for x, we can use the quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

In this case, a = 1, b = 0, and c = -18. Substituting these values into the quadratic formula, we get:

x = [0 ± √(0² - 4 * 1 * -18)] / 2 * 1

Simplifying further: x = ± √72 / 2

x = ± 6√2 / 2

x = ± 3√2

5. Solution

Therefore, the solutions to the equation (x+5)(x-5) = -7 are:

x = 3√2

x = -3√2

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