## anonymous 4 years ago How do I solve by completing the square. Express the solutions in simplest radical form: 1/2x^2 + x - 13 = 0?

1. anonymous

Easy to re-write it as: x^2 + 2x - 26 = 0 Then, completing a square will give you: x^2 + 2x + 1 - 27 = 0 (x+1)^2 = 27

2. anonymous

The answer is supposed to be $-1 +/- 3\sqrt{3}$

3. anonymous

'cause I got x = -1 +/- √105 / 4

4. anonymous

Well, when (x+1)^2 = 27, you do get: x + 1 = +/- SQRT(27) x + 1 = +/- 3*SQRT(3) x = -1 + 3 * SQRT(3) OR x = -1 - 3 * SQRT(3)

$(x+1)^{2}=27$$(x+1) =\sqrt{27}$$x = -1 \pm \sqrt{27}$$x = -1\pm \sqrt{9}\sqrt{3}$$x=-1\pm3\sqrt{3}$Do you see how GT answers is the same as your book's answer?