(x%2B7)%3D0.jpeg "(x-8)(x+7)=0")
Solving the Equation (x-8)(x+7) = 0
This equation is a simple quadratic equation in factored form. To solve for x, we can use the Zero Product Property, which states:
If the product of two or more factors is zero, then at least one of the factors must be zero.
Applying this to our equation, we have:
- (x-8) = 0
- (x+7) = 0
Now, we solve each of these individual equations:
- x - 8 = 0 => x = 8
- x + 7 = 0 => x = -7
Therefore, the solutions to the equation (x-8)(x+7) = 0 are x = 8 and x = -7.
In other words, these are the values of x that make the entire equation true.
Let's check our solutions by plugging them back into the original equation:
- For x = 8: (8-8)(8+7) = 0 * 15 = 0 (True)
- For x = -7: (-7-8)(-7+7) = -15 * 0 = 0 (True)
Both solutions satisfy the equation, confirming our answers.