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Solving the Equation (x+7)(x-2)=90
This article will guide you through the process of solving the equation (x+7)(x-2)=90.
Step 1: Expand the Left Side
First, we need to expand the left side of the equation by multiplying the two binomials using the FOIL method (First, Outer, Inner, Last):
(x+7)(x-2) = x² - 2x + 7x - 14
Simplifying the equation, we get:
x² + 5x - 14 = 90
Step 2: Move the Constant Term to the Left Side
To get a standard quadratic equation, we need to move the constant term (90) to the left side by subtracting 90 from both sides:
x² + 5x - 14 - 90 = 0
This simplifies to:
x² + 5x - 104 = 0
Step 3: Factor the Quadratic Equation
Now we have a quadratic equation in standard form (ax² + bx + c = 0). We can solve this equation by factoring.
We need to find two numbers that multiply to -104 and add up to 5. The numbers 13 and -8 satisfy these conditions.
Therefore, we can factor the quadratic equation as:
(x + 13)(x - 8) = 0
Step 4: Solve for x
For the product of two factors to be zero, at least one of the factors must be zero. So, we have two possible solutions:
- x + 13 = 0 => x = -13
- x - 8 = 0 => x = 8
Conclusion
Therefore, the solutions to the equation (x+7)(x-2)=90 are x = -13 and x = 8.