Question

Solve x² - 8x + 5 = 0 using the completing-the-square method.

Answer 1

Answer:  $\text{x} = 4\pm\sqrt{11}$

This is the same as writing $\text{x} = 4+\sqrt{11}\ \text{ or } \ \text{x} = 4-\sqrt{11}$

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Work Shown:

$\text{x}^2 - 8\text{x} + 5 = 0\\\\\text{x}^2 - 8\text{x} = -5\\\\\text{x}^2 - 8\text{x} + 16 = -5+16\\\\(\text{x}-4)^2 = 11\\\\\text{x}-4 = \pm\sqrt{11}\\\\\text{x} = 4\pm\sqrt{11}$

In the third step, I added 16 to both sides so I could complete the square and factor. The 16 is from first dividing the x coefficient -8 in half (to get -4). Then square that result to get (-4)^2 = 16

You can use the quadratic formula to verify each root.