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Are use factoring to solve the quadratic equation. Check by substitution or by using a graph utility and identifying X interceptsFind the solution set

Are use factoring to solve the quadratic equation. Check by substitution or by using-example-1

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S=\lbrace-4,8\rbrace

1) Let's factor this quadratic equation. Note that we need to find the sum of two numbers whose sum is -4, and the product equal to -32


\begin{gathered} S=-8+4=-4 \\ P=-8*4=-32 \end{gathered}

2) So let's rewrite 4x as the sum of -8 and -4:


\begin{gathered} x^2-8x+4x-32 \\ x(x-8)+4(x-8) \\ (x+4)(x-8) \end{gathered}

So let's find the roots equation for each factor above to zero:


\begin{gathered} (x+4)=0,x=-4 \\ x-8=0,x=8 \\ S=\mleft\lbrace-4,8\mright\rbrace \end{gathered}

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