Question

Solve each equation by using the square root property. X^2–16x+64=8

Answer 1

Explanation:

`(x-8)^(2)`=-8

Answer 2

X^2–16x+64=8

Subtract 8 from both sides of the equation:

X^2–16x+64 -8=8-8

X^2–16x+56=0

Apply the quadratic formula:

`\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Where:

a=1 . b=-16 , c = 56

Replacing:

`\frac{16\pm\sqrt[]{(-16)^2-4(1*56)}}{2*1}`
`\frac{16\pm\sqrt[]{256-224}}{2}`
`\frac{16\pm\sqrt[]{32}}{2}`

positive:

`\frac{16+\sqrt[]{32}}{2}=\frac{16+4\sqrt[]{2}}{2}\text{ = }8+2\sqrt[]{2}`

Negative:

`\frac{16-\sqrt[]{32}}{2}\text{ =}\frac{16-4\sqrt[]{2}}{2}=8-2\sqrt[]{2}`