(x-9)-0.jpeg "(x+3)(x-9) 0")
Solving the Equation (x+3)(x-9) = 0
This equation represents a quadratic expression set equal to zero. Solving this equation will give us the values of 'x' that make the expression true. Here's how to solve it:
Understanding the Zero Product Property
The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.
In our equation, (x+3) and (x-9) are the two factors. Therefore, to make the product equal to zero, either (x+3) must equal zero OR (x-9) must equal zero.
Solving for x
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Set each factor equal to zero:
- x + 3 = 0
- x - 9 = 0
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Solve for x in each equation:
- x = -3
- x = 9
The Solution
Therefore, the solutions to the equation (x+3)(x-9) = 0 are x = -3 and x = 9.
Verification
We can verify our solutions by substituting them back into the original equation:
- For x = -3: (-3 + 3)(-3 - 9) = (0)(-12) = 0
- For x = 9: (9 + 3)(9 - 9) = (12)(0) = 0
Both solutions make the equation true.