Question

How do you solve the quadratic equation by completing the square: `v^2+6v-59=0`?

Answer 1

`^v^2+6v-59 =0`
`color(white)("XXXX")` `rarr` `color(white)("XXXX")` `v=-3+-2sqrt(17)`
`color(white)("XXXX")`(by completing the square)

Explanation:

`v^2+6v-59 = 0`
`color(white)("XXXX")`Move the constant to the right side (out of the way)
`v^2+6v = 59`
`color(white)("XXXX")`Add as the third term the value needed to make the right side a square
`v^2+6v+3^2 = 59+9`
`color(white)("XXXX")`Re-write right side as a squared binomial
`(v+3)^2 = 68`
`color(white)("XXXX")`Take the square root of both sides
`v+3 = +-sqrt(68) = +-2sqrt(17)`
`color(white)("XXXX")`Isolate `v` by subtracting `3` from both sides
`v = -3+-2sqrt(17)`