Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 564: 17

$x=10.7,-28.7$

$x^2+18x=307$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=18$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(18)^2}{4}=81$ To complete the square, add $4$ on both sides. $x^2+18x+81=307+81$ $\implies (x+9)^2=388$ $\implies x+9=19.7$ and $\implies x+9=-19.7$ or, $x=10.7,-28.7$