# Algebra - Completing the Square on Monic Expressions

a - answer    s - solution    v - video    d - discussion

## Question 1

What number should be added in order to form a perfect square?

a) $x^2+2x+\square$a s v d
b) $x^2+4x+\square$a s v d
c) $x^2+10x+\square$a s v d
d) $x^2+20x+\square$a s v d
e) $x^2+8x+\square$a s v d
f) $x^2+12x+\square$a s v d
g) $x^2+22x+\square$a s v d
h) $x^2+30x+\square$a s v d

## Question 2

What number should be added in order to form a perfect square? Leave answers as top-heavy/improper fractions where necessary

a) $x^2+3x+\square$a s v d
b) $x^2+5x+\square$a s v d
c) $x^2+9x+\square$a s v d
d) $x^2+7x+\square$a s v d
e) $x^2+x+\square$a s v d
f) $x^2+11x+\square$a s v d
g) $x^2+13x+\square$a s v d
h) $x^2+15x+\square$a s v d

## Question 3

What number should be added in order to form a perfect square? Leave answers as top-heavy/improper fractions where necessary

a) $x^2-2x+\square$a s v d
b) $x^2-4x+\square$a s v d
c) $x^2-8x+\square$a s v d
d) $x^2-3x+\square$a s v d
e) $x^2-7x+\square$a s v d
f) $x^2-11x+\square$a s v d
g) $x^2-18x+\square$a s v d
h) $x^2-13x+\square$a s v d

## Question 4

Complete the square

a) $x^2+4x+5$a s v d
b) $x^2+6x+10$a s v d
c) $x^2+10x+28$a s v d
d) $x^2+16x+70$a s v d
e) $x^2+20x+120$a s v d
f) $x^2+8x+16$a s v d
g) $x^2+12x+50$a s v d
h) $x^2+18x+110$a s v d

## Question 5

Complete the square

a) $x^2+6x+8$a s v d
b) $x^2+8x+12$a s v d
c) $x^2+12x+33$a s v d
d) $x^2+14x+39$a s v d
e) $x^2+10x+12$a s v d
f) $x^2+16x+64$a s v d
g) $x^2+2x-1$a s v d
h) $x^2+18x-219$a s v d

## Question 6

Complete the square

a) $x^2-6x+11$a s v d
b) $x^2-10x+29$a s v d
c) $x^2-8x+26$a s v d
d) $x^2-18x+114$a s v d
e) $x^2-22x+138$a s v d
f) $x^2-4x+1$a s v d
g) $x^2-2x-5$a s v d
h) $x^2-22x+76$a s v d

## Question 7

Complete the square. Leave answers as top-heavy/improper fractions where necessary

a) $x^2+3x+3$a s v d
b) $x^2+5x+7$a s v d
c) $x^2+9x+20$a s v d
d) $x^2+x+5$a s v d
e) $x^2+7x+10$a s v d
f) $x^2+11x+25$a s v d
g) $x^2+3x-4$a s v d
h) $x^2+9x-\frac34$a s v d

## Question 8

Complete the square. Leave answers as top-heavy/improper fractions where necessary

a) $x^2-3x+4$a s v d
b) $x^2-7x+10$a s v d
c) $x^2-5x+2$a s v d
d) $x^2-x+7$a s v d
e) $x^2-11x$a s v d
f) $x^2-3x+\frac34$a s v d
g) $x^2-5x-\frac58$a s v d
h) $x^2-13x+12.5$a s v d

## Question 9

Complete the square

a) $x^2+\frac12x+1$a s v d
b) $x^2+\frac43x$a s v d
c) $x^2-\frac74x+15$a s v d
d) $x^2+0.2x+1$a s v d
e) $x^2+1.2x-2$a s v d
f) $x^2-0.3x+0.5$a s v d
g) $x^4-2x^2+5$a s v d
h) $x^6+\frac14x^3-\frac45$a s v d