Answer
Given: $x^2+20x$
The coefficient of the $x$-term is $20$. Half of $20$ is $10$, and $(10)^2 = 100$ Thus, add $100$ to both sides to complete the square.
$x^2+20x+100=100$
Since, $a^2+2ab+b^2=(a+b)^2$, the equation becomes $(x+10)^2=100$
Apply the square root property to get the value of $x$.
$x+10=±\sqrt{100}$
$x=-10±10$
$x=10+10$ or $x=10-10$
$x=20$ or $x=0$
Work Step by Step
Given: $x^2+20x$
The coefficient of the $x$-term is $20$. Half of $20$ is $10$, and $(10)^2 = 100$ Thus, add $100$ to both sides to complete the square.
$x^2+20x+100=100$
Since, $a^2+2ab+b^2=(a+b)^2$, the equation becomes $(x+10)^2=100$
Apply the square root property to get the value of $x$.
$x+10=±\sqrt{100}$
$x=-10±10$
$x=10+10$ or $x=10-10$
$x=20$ or $x=0$
