(x-1)%3D120.jpeg "(x+6)(x-1)=120")
Solving the Equation (x+6)(x-1) = 120
This equation involves a quadratic expression, and we need to solve for the values of 'x' that satisfy the equation. Here's a step-by-step approach:
1. Expand the Equation
First, we expand the left side of the equation by multiplying the two binomials:
(x + 6)(x - 1) = x² + 5x - 6
Now the equation looks like this:
x² + 5x - 6 = 120
2. Move all terms to one side
To solve a quadratic equation, we need it in standard form (ax² + bx + c = 0). So, subtract 120 from both sides:
x² + 5x - 126 = 0
3. Factor the Quadratic Expression
The next step is to factor the quadratic expression on the left-hand side. We need to find two numbers that add up to 5 (the coefficient of the x term) and multiply to -126 (the constant term). These numbers are 14 and -9:
(x + 14)(x - 9) = 0
4. Solve for x
For the product of two factors to equal zero, at least one of the factors must be zero. Therefore, we have two possible solutions:
- x + 14 = 0 => x = -14
- x - 9 = 0 => x = 9
Conclusion
The solutions to the equation (x+6)(x-1) = 120 are x = -14 and x = 9.