Algebra - Completing the Square Review Questions

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Question 1


Complete the square on the following

a) $x^2+6x+7$a s v d
b) $x^2+8x+20$a s v d
c) $x^2+12x+25$a s v d
d) $x^2+2x+9$a s v d
e) $x^2-10x+15$a s v d
f) $x^2-14x+1$a s v d


Question 2


Solve by completing the square

a) $x^2+10x+21=0$a s v d
b) $x^2+16x+48=0$a s v d
c) $x^2+22x+57=0$a s v d
d) $x^2+4x=0$a s v d
e) $x^2-18x-19=0$a s v d
f) $x^2-2x-8=0$a s v d


Question 3


Complete the square on the following

a) $x^2+3x+1$a s v d
b) $x^2+5x-1$a s v d
c) $x^2+9x+\frac14$a s v d
d) $x^2+x+2\frac14$a s v d
e) $x^2-7x-5$a s v d
f) $x^2-x+\frac{71}{4}$a s v d


Question 4


Solve by completing the square

a) $x^2+3x+2=0$a s v d
b) $x^2+7x+12=0$a s v d
c) $x^2+11x+28=0$a s v d
d) $x^2-5x-6=0$a s v d
e) $x^2-x-42=0$a s v d
f) $x^2-3x+\frac54$a s v d


Question 5


Complete the square on the following

a) $2x^2+12x+5$a s v d
b) $3x^2+12x-8$a s v d
c) $5x^2+10x-1$a s v d
d) $4x^2-24x+19$a s v d
e) $7x^2-56x+13$a s v d
f) $11x^2-22x-15$a s v d


Question 6


Solve by completing the square

a) $2x^2+8x+6=0$a s v d
b) $3x^2+24x+45=0$a s v d
c) $4x^2+8x+3=0$a s v d
d) $9x^2+18x-7=0$a s v d
e) $2x^2+9x+4=0$a s v d
f) $6x^2-7x-20=0$a s v d


Question 7


Complete the square on the following

a) $5x^2+20x+\frac{5}{4}$a s v d
b) $8x^2+24x+\frac{3}{2}$a s v d
c) $6x^2+5x+\frac{2}{3}$a s v d
d) $2x^2+2x+\frac{1}{2}$a s v d
e) $7x^2+4x+1$a s v d
f) $11x^2-2x-\frac{5}{11}$a s v d


Question 8


Solve by completing the square

a) $3x^2-\frac{x}{2}-1=0$a s v d
b) $6x^2+13x+6=0$a s v d
c) $20x^2+\frac{1}{2}x-\frac{1}{4}=0$a s v d
d) $8x^2+\frac{18x}{5}-\frac{9}{5}=0$a s v d
e) $10x^2-3x+\frac{2}{9}=0$a s v d
f) $\frac{x^2}{2}+\frac{8x}{3}-2=0$a s v d