Question
Solve $\color{blue}{-x^2+2x+7 = 0}$ using factoring.
Answer
$$ \color{blue}{ x_1 = 1-2 \sqrt{ 2 } }~~ \text{and}~~ \color{blue}{ x_2 = 1+2 \sqrt{ 2 } } $$
Explanation
First we need to factor trinomial $ \color{blue}{ -x^2+2x+7 } $ and than we use factored form to solve an equation $ \color{blue}{ -x^2+2x+7 = 0} $.
Step 1: We can simplify equation by multiplying both sides by -1. After multiplying we have the following equation:
$$ \begin{aligned} -x^2+2x+7 &= 0 \,\,\, / \color{orangered}{\cdot \, -1 } \\[0.9 em ] x^2-2x-7 &=0 \end{aligned} $$Since the quadratic trinomial cannot be factored out we solved the problem using quadratic formula.
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