# Quadratics: Completing the Square Practice AK

Solve the following quadratic equations by completing the square:

1.

\eqalign{x^2+6x&=0\\x^2+6x+9&=9\\(x+3)^2&=9\\\sqrt{(x+3)^2}&=\sqrt{9}\\x+3=3 &\qquad x+3=-3\\x=0 &\qquad x=-6}

2.

\eqalign{x^2-8x&=0\\x^2-8x+16&=16\\(x-4)^2&=16\\\sqrt{(x-4)^2}&=\sqrt{16}\\x-4=4 &\qquad x-4=-4\\x=8 &\qquad x=0}

3.

\eqalign{x^2-20x=0\\x^2-20x+100&=100\\(x-10)^2&=100\\\sqrt{(x-10)^2}&=\sqrt{100}\\x-10=10 &\qquad x-10=-10\\x=20 &\qquad x=0}

4.

\eqalign{x^2+30x=0\\x^2+30x+225&=225\\(x+15)^2&=225\\\sqrt{(x+15)^2}&=\sqrt{225}\\x+15=15 &\qquad x+15=-15\\x=0 &\qquad x=-30}

5.

\eqalign{x^2-2x=0\\x^2-2x+1&=1\\(x-1)^2&=1\\\sqrt{(x-1)^2}&=\sqrt{1}\\x-1=1 &\qquad x-1=-1\\x=2 &\qquad x=0}

6.

\eqalign{x^2+2x-24=0\\x^2+2x&=24\\x^2+2x+1=25\\(x+1)^2&=25\\\sqrt{(x+1)^2}&=\sqrt{25}\\x+1=5 &\qquad x+1=-5\\x=4 &\qquad x=-6}

7.

\eqalign{x^2+12x+11=0\\x^2+12x&=-11\\x^2+12x+36=25\\(x+6)^2&=25\\\sqrt{(x+6)^2}&=\sqrt{25}\\x+6=5 &\qquad x+6=-5\\x=-1 &\qquad x=-11}

8.

\eqalign{x^2+3x=0\\x^2+3x&+2.25=2.25\\(x+1.5)^2&=2.25\\\sqrt{(x+1.5)^2}&=\sqrt{2.25}\\x+1.5=1.5 &\qquad x+1.5=-1.5\\x=0 &\qquad x=-3}

9.

\eqalign{x^2-4x=5\\x^2-4x&+4=9\\(x-2)^2&=9\\\sqrt{(x-2)^2}&=\sqrt{9}\\x-2=3 &\qquad x-2=-3\\x=5 &\qquad x=-1}

10.

\eqalign{x^2-14x=51\\x^2-14x&+49=100\\(x-7)^2&=100\\\sqrt{(x-7)^2}&=\sqrt{100}\\x-7=10 &\qquad x-7=-10\\x=17 &\qquad x=-3}