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Solve the following problem for the roots by using the quadratic formula.
2(6 - x) = x(x + 5)

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Answer:

The roots are [tex]x=\dfrac{-7+ \sqrt{97}}{2}\text{ and }x=\dfrac{-7- \sqrt{97}}{2}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]2(6 - x) = x(x + 5)[/tex]

Remove the parenthesis and simplify.

[tex]12-2 x= x^2 + 5x[/tex]

[tex]x^2+7x-12=0[/tex]

Now use the quadratic formula [tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].

Susbtitute a=1, b=7 and c=-12 in above formula.

[tex]x=\dfrac{-7\pm \sqrt{7^2-4(1)(-12)}}{2(1)}[/tex]

[tex]x=\dfrac{-7\pm \sqrt{49+48}}{2}[/tex]

[tex]x=\dfrac{-7\pm \sqrt{97}}{2}[/tex]

Hence, the roots are [tex]x=\dfrac{-7+ \sqrt{97}}{2}\text{ and }x=\dfrac{-7- \sqrt{97}}{2}[/tex].

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