Multiple Choice
Solve the given quadratic equation by completing the square.
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1. Equations and Inequalities
Completing the Square
Multiple Choice
Solve the given quadratic equation by completing the square.
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Verified step by step guidance1
Start by rewriting the quadratic equation in the form \(x^2 + 3x - 5 = 0\). To complete the square, we need to focus on the terms involving \(x\).
Move the constant term to the other side of the equation: \(x^2 + 3x = 5\).
To complete the square, take half of the coefficient of \(x\), which is \(\frac{3}{2}\), and square it to get \(\left(\frac{3}{2}\right)^2 = \frac{9}{4}\). Add and subtract this value inside the equation: \(x^2 + 3x + \frac{9}{4} = 5 + \frac{9}{4}\).
Rewrite the left side as a perfect square trinomial: \((x + \frac{3}{2})^2 = \frac{29}{4}\).
Solve for \(x\) by taking the square root of both sides: \(x + \frac{3}{2} = \pm \sqrt{\frac{29}{4}}\). Then, isolate \(x\) to find the solutions: \(x = -\frac{3}{2} \pm \frac{\sqrt{29}}{2}\).
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