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Algebra - Completing the Square on Monic Expressions

  a - answer    s - solution    v - video

Question 1


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

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


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


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


Question 4


Complete the square

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


Question 5


Complete the square

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


Question 6


Complete the square

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


Question 7


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

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


Question 8


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

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


Question 9


Complete the square

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