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Solving the Quadratic Equation (x-3)(x+4)=8
This article will guide you through the steps of solving the quadratic equation (x-3)(x+4)=8.
1. Expanding the Equation
First, we need to expand the left side of the equation by multiplying the binomials:
(x-3)(x+4) = x² + x - 12
Now our equation becomes:
x² + x - 12 = 8
2. Rearranging the Equation
To solve this quadratic equation, we need to set it equal to zero. Subtract 8 from both sides:
x² + x - 20 = 0
3. Factoring the Equation
Now we need to factor the quadratic expression. We are looking for two numbers that add up to 1 (the coefficient of the x term) and multiply to -20 (the constant term). These numbers are 5 and -4.
Therefore, we can factor the equation as:
(x + 5)(x - 4) = 0
4. Solving for x
For the product of two factors to be zero, at least one of them must be zero. So, we have two possible solutions:
- x + 5 = 0 => x = -5
- x - 4 = 0 => x = 4
Conclusion
The solutions to the quadratic equation (x-3)(x+4)=8 are x = -5 and x = 4.