To solve the equation x² – 12 – 7x = 0 using the Zero Product Property, we first need to rearrange the equation into a standard quadratic form:
x² – 7x – 12 = 0
Now, we can factor this quadratic expression. We want two numbers that multiply to -12 (the constant term) and add to -7 (the coefficient of the x term). The numbers -8 and 1 fit this requirement because:
- -8 * 1 = -8
- -8 + 1 = -7
Thus, we can factor the equation as follows:
(x – 8)(x + 1) = 0
Next, we apply the Zero Product Property, which states that if the product of two factors equals zero, at least one of the factors must equal zero. Therefore, we set each factor equal to zero:
x – 8 = 0 and x + 1 = 0
Solving these equations gives:
- x = 8
- x = -1
Thus, the solutions to the equation x² – 12 – 7x = 0 are:
- x = 8
- x = -1