Answer
$x^2 + 6x + 8 = 0$
Subtract $8$ to both sides to isolate the binomial $x^2 + 6x$.
$x^2 + 6x + 8 -8= 0-8$
$x^2 + 6x = -8$
Determine the coefficient of the x-term, which in this example is $6$. Half of $6$ is $3$, and $3^2$ is $9$.
Thus, add $9$ to both sides of the equation to complete the square:
$x^2 + 6x +9 = -8+9$
$x^2 + 6x +9= 1$
$(x +3)^2 = 1$
Use the Square Root Property, $u^2 = d$, then $u = \sqrt d$ or $u = - \sqrt d$ to solve for $x$.
$(x +3)^2 = 1$
$x +3 = ±\sqrt 1$
$x = -3 ±\sqrt 1$
$x = -2$ or $x=-4$
Work Step by Step
$x^2 + 6x + 8 = 0$
Subtract $8$ to both sides to isolate the binomial $x^2 + 6x$.
$x^2 + 6x + 8 -8= 0-8$
$x^2 + 6x = -8$
Determine the coefficient of the x-term, which in this example is $6$. Half of $6$ is $3$, and $3^2$ is $9$.
Thus, add $9$ to both sides of the equation to complete the square:
$x^2 + 6x +9 = -8+9$
$x^2 + 6x +9= 1$
$(x +3)^2 = 1$
Use the Square Root Property, $u^2 = d$, then $u = \sqrt d$ or $u = - \sqrt d$ to solve for $x$.
$(x +3)^2 = 1$
$x +3 = ±\sqrt 1$
$x = -3 ±\sqrt 1$
$x = -2$ or $x=-4$
