# Algebra - Solving Monic Quadratics By Completing The Square

a - answer    s - solution    v - video

## Question 1

Solve. Remember there are two solutions

a) $x^2=9$a s v
b) $x^2=16$a s v
c) $x^2=49$a s v
d) $x^2=81$a s v
e) $x^2=121$a s v
f) $x^2=400$a s v

## Question 2

Solve

a) $(x-5)^2=0$a s v
b) $(x-8)^2=0$a s v
c) $(x+3)^2=0$a s v
d) $(x+7)^2=0$a s v
e) $(x-12)^2=0$a s v
f) $(x+67)^2=0$a s v

## Question 3

Solve

a) $x^2+6x+9=0$a s v
b) $x^2+10x+25=0$a s v
c) $x^2+16x+64=0$a s v
d) $x^2-6x+9=0$a s v
e) $x^2-2x+1=0$a s v
f) $x^2-20x+100=0$a s v

## Question 4

Solve. Remember there are two solutions

a) $(x-2)^2=25$a s v
b) $(x-5)^2=36$a s v
c) $(x-9)^2=81$a s v
d) $(x+1)^2=100$a s v
e) $(x+7)^2=49$a s v
f) $(x+14)^2=144$a s v

## Question 5

Solve by forming a perfect square on the left hand side

a) $x^2+8x+16=25$a s v
b) $x^2+12x+36=64$a s v
c) $x^2+22x+121=9$a s v
d) $x^2-4x+4=1$a s v
e) $x^2-14x+49=100$a s v
f) $x^2-24x+144=49$a s v

## Question 6

Solve by completing the square

a) $x^2+10x+21=0$a s v
b) $x^2+6x+8=0$a s v
c) $x^2+16x+39=0$a s v
d) $x^2-18x-19=0$a s v
e) $x^2-2x-63=0$a s v
f) $x^2-22x-23=0$a s v

## Question 7

Solve. Remember there are two solutions

a) $x^2=\frac19$a s v
b) $x^2=\frac{1}{25}$a s v
c) $x^2=\frac{1}{4}$a s v
d) $x^2=\frac{9}{16}$a s v
e) $x^2=\frac{25}{64}$a s v
f) $x^2=\frac{121}{49}$a s v

## Question 8

Solve

a) $(x+1)^2=\frac19$a s v
b) $(x-4)^2=\frac{4}{25}$a s v
c) $\left(x+\frac12\right)^2=\frac{9}{16}$a s v
d) $(x+2)^2-\frac{1}{36}=0$a s v
e) $(x-1)^2-\frac{4}{49}=0$a s v
f) $\left(x+\frac23\right)^2-\frac{1}{81}=0$a s v

## Question 9

Solve by completing the square

a) $x^2+3x-4=0$a s v
b) $x^2+x-2=0$a s v
c) $x^2-5x-6=0$a s v
d) $x^2-7x+6=0$a s v
e) $x^2-x-20=0$a s v
f) $x^2-x-\frac{63}{4}=0$a s v

## Question 10

Solve by completing the square

a) $x^2+3x+\frac{35}{16}=0$a s v
b) $x^2-x+\frac{5}{36}=0$a s v
c) $x^2-7x+\frac{187}{16}=0$a s v
d) $x^2+9x+\frac{713}{36}=0$a s v
e) $x^2-11x+\frac{2989}{100}=0$a s v
f) $x^2-13x+\frac{3969}{100}=0$a s v

## Question 11

Solve by completing the square

a) $x^2+\frac32x+\frac12=0$a s v
b) $x^2+\frac92x+2=0$a s v
c) $x^2+\frac13x-\frac23=0$a s v
d) $x^2-\frac53x-\frac{14}{9}=0$a s v
e) $x^2-\frac65x-\frac{27}{25}=0$a s v
f) $x^2-\frac75x-\frac{3}{20}=0$a s v

## Question 12

Solve. Remember there are two solutions

a) $x^2=2$a s v
b) $x^2=6$a s v
c) $x^2=11$a s v
d) $x^2=8$a s v
e) $x^2=18$a s v
f) $x^2=45$a s v

## Question 13

Solve

a) $(x-2)^2=2$a s v
b) $(x-7)^2=5$a s v
c) $(x+3)^2-15=0$a s v
d) $\left(x+\sqrt2\right)^2=2$a s v
e) $\left(x-\sqrt3\right)^2=27$a s v
f) $\left(x+2\sqrt7\right)^2-112$a s v

## Question 14

Solve by completing the square

a) $x^2+6x+7=0$a s v
b) $x^2-4x+1=0$a s v
c) $x^2+14x+39=0$a s v
d) $x^2-2x-5=0$a s v
e) $x^2-10x+17=0$a s v
f) $x^2+16x-11=0$a s v

## Question 15

Solve by completing the square

a) $x^2+5x+\frac{11}{2}=0$a s v
b) $x^2+x-1=0$a s v
c) $x^2-7x+\frac{19}{2}=0$a s v
d) $x^2-x+\frac{1}{36}=0$a s v
e) $x^2-\frac52x+\frac54=0$a s v
f) $x^2+\frac56x-\frac{1103}{225}=0$a s v

## Question 16

Solve by completing the square

a) $x^2+2\sqrt2x-6=0$a s v
b) $x^2-2\sqrt3x-105=0$a s v
c) $x^2-4\sqrt5x+15=0$a s v
d) $x^2-\sqrt{72}x-14=0$a s v
e) $x^2-\sqrt{2}x-\frac14=0$a s v
f) $x^2+\sqrt5x+\frac{117}{100}=0$a s v

## Question 17

Solve by completing the square

a) $x^2=16-6x$a s v
b) $y^2-39=10y$a s v
c) $x(2x+1)=x^2+78\frac34-2x$a s v
d) $x+5+\frac{9}{4x}=0$a s v
e) $x^2\left(\frac12+\frac{\sqrt5}{x}\right)=20$a s v
f) $1=\frac{17-8z\sqrt3}{16z^2}$a s v