(x-9)%3D0-standard-form.jpeg "(x-6)(x-9)=0 Standard Form")
Solving the Equation (x-6)(x-9) = 0 and Converting to Standard Form
This equation is already in a factored form, making it easy to solve for the values of x. Here's how to do it:
1. Zero Product Property:
The equation is based on the Zero Product Property which states that if the product of two or more factors is zero, then at least one of the factors must be zero.
2. Solve for x:
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For the first factor (x-6), set it equal to zero: x - 6 = 0 x = 6
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For the second factor (x-9), set it equal to zero: x - 9 = 0 x = 9
Therefore, the solutions to the equation (x-6)(x-9) = 0 are x = 6 and x = 9.
3. Standard Form:
The standard form of a quadratic equation is ax² + bx + c = 0. To get our equation into standard form, we need to expand the factored form:
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Expand the factors: (x-6)(x-9) = x² - 9x - 6x + 54
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Combine like terms: x² - 15x + 54 = 0
Therefore, the standard form of the equation (x-6)(x-9) = 0 is x² - 15x + 54 = 0.