8.9.4 Solving More Quadratic Equations

Algebra 18.9.4 Solving More Quadratic Equations

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Solve each equation by rewriting it in factored form and using the zero product property. Be prepared to explain your reasoning.

$x^{2} + 12 x + 11 = 0$

Compare your answer:

$x = - 1$ and $x = - 11$

The equation $x^{2} + 12 x + 11 = 0$ can be written as $(x + 11) (x + 1) = 0$ , which means $x + 11 = 0$ or $x + 1 = 0$ .

$x^{2} - 3 = 1$

Compare your answer:

$x = - 2$ and $x = 2$

The equation $x^{2} - 3 = 1$ can be written as $x^{2} - 4 = 0$ , which is $(x + 2) (x - 2) = 0$ , which means $x + 2 = 0$ or $x - 2 = 0$ .

$x^{2} - 6 x + 7 = - 2$

Compare your answer:

$x = 3$

The equation $x^{2} - 6 x + 7 = - 2$ can be written as $x^{2} - 6 x + 9 = 0$ , which is $(x - 3) (x - 3) = 0$ , which means $x - 3 = 0$ .

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