(x-5)%3D-7.jpeg "(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