(x-1)%3D128.jpeg "(x+7)(x-1)=128")
Solving the Quadratic Equation: (x+7)(x-1) = 128
This article will guide you through the steps of solving the quadratic equation (x+7)(x-1) = 128.
Expanding the Equation
First, we need to expand the left side of the equation by multiplying the two binomials:
(x+7)(x-1) = x² + 6x - 7
Now, our equation is: x² + 6x - 7 = 128
Bringing it to Standard Form
To solve the quadratic equation, we need to bring it to standard form, which is:
ax² + bx + c = 0
Subtracting 128 from both sides, we get:
x² + 6x - 135 = 0
Solving the Quadratic Equation
Now, we have a quadratic equation in standard form. We can solve this equation using the quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
Where a = 1, b = 6, and c = -135.
Plugging these values into the quadratic formula, we get:
x = [-6 ± √(6² - 4 * 1 * -135)] / 2 * 1
x = [-6 ± √(636)] / 2
x = [-6 ± 2√159] / 2
Simplifying the expression, we get two solutions:
x = -3 + √159 x = -3 - √159
Conclusion
Therefore, the solutions to the quadratic equation (x+7)(x-1) = 128 are x = -3 + √159 and x = -3 - √159.