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Question

# Solve each equation using the quadratic formula. Round to the nearest hundredth. -x² + 9x + 5 = -3

Solution

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Given equation

$-x^2+9x+5=0.$

Write the equation in standard form then equation becomes $-x^2+9x+8=0$. Identify a,b and c in the equation. So a=-1, b=9 and c=8. Use the quadratic formula $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$.

\begin{align*} x&=\dfrac{-9\pm\sqrt{(9)^2-4(-1)(8)}}{2(-1} \text{ substitute the values of a,b and c}\\ &=\dfrac{-9\pm\sqrt{81+32}}{-2}\\ &=\dfrac{-9\pm\sqrt{113}}{-2}\\ &=\dfrac{-9+\sqrt{113}}{-2} \text{ and} \dfrac{-9-\sqrt{113}}{-2}\\ x&\approx-0.82 \text{ and } x\approx 9.82 \end{align*}

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