Question

Solve by completing the square
x^2+7x-8=0

Answer 1

add 8 to both sides
\[\implies x^2 + 7x = 8\]
now divide 7 by 2 and square it
\[\implies x^2 + 7x + \left ( \frac 72 \right) ^2 = 8 + \left(\frac 72 \right)^2\]
simplify
\[\implies x^2 + 7x + \frac{49}4 = 8 + \frac{49}4\]
combine like terms...
\[\implies x^2 + 7x + \frac {49}{4} = \frac{81}{4}\]
factor out...
\[\implies (x + \frac 72)^2 = \frac{81}4\]
take square root of bot sides
\[\implies x + \frac 72 = \pm \frac 92\]
subtract both sides by 7/2
\[\implies x = \pm \frac 92 - \frac 72\]
simpify to get final answer


does that help?