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Chapter 0: Problem 74

Solve each quadratic equation by completing the square. $$x^{2}+6 x-5=0$$

Short Answer

Expert verified
The solutions to the equation are \( x = -3 + \sqrt{14}\) and \(x = -3 - \sqrt{14}\)

Step by step solution

01

Rearrange the Quadratic Equation

Write the quadratic equation in the form \(x^{2} + 6x = 5\). This makes completing the square process easier.
02

Complete the Square

In order to complete the square, we need to take half of the coefficient of x, square it and add and subtract it on the left hand side of the equation. This gives us \((x^{2}+6x + 9) - 9 = 5\), which can be simplified to \((x+3)^{2} - 9 = 5\)
03

Solve for x

Moving to the final stage of the solution, this involves getting x alone by first adding 9 from both sides and then taking the square root on both sides. This will result in \(x = -3 \pm \sqrt{14}\).
04

Verify your Answers

These solutions can be confirmed by substituting back into the original equation to make sure it holds.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$x^{3}-64=(x+4)\left(x^{2}+4 x-16\right)$$

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