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Question

# Solve each equation by using the Square Root Property. Round to the nearest hundredth if necessary. $x^{2}+7 x+\frac{49}{4}=4$

Solution

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Step 1
1 of 2

Determine the solutions to the equation.

\begin{align*} \left(x + \dfrac{7}{2} \right)^{2} & = 4 && {\text {factor the perfect square trinomial}} \\ \sqrt {\left(x + \dfrac{7}{2} \right)^{2}} & = \sqrt{4} && {\text {square root property}} \\ x + \dfrac{7}{2} & = \pm 2 \\ x + \dfrac{7}{2} - \dfrac{7}{2} & = -\dfrac{7}{2} \pm 2 && {\text {subtract \dfrac{7}{2} from both sides of the equation}} \\ x & = - \dfrac{7}{2} \pm 2 && {\text {solutions to the equation}} \\\\ x & = -\dfrac{7}{2} + 2 = -\dfrac{3}{2} && {\text {write as two equations to simplify}}\\ x & = -\dfrac{7}{2} - 2 = -\dfrac{11}{2} \end{align*}

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