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Algebra - Solving Non-Monic Quadratics by Completing the Square

  a - answer    s - solution    v - video

Question 1


Solve. Remember there are two solutions

a) $2x^2=50$  a s v
b) $3x^2=27$  a s v
c) $7x^2=112$  a s v
d) $\frac12x^2=2$  a s v
e) $0.4x^2=0.4$  a s v
f) $\frac{245}{x^2}=5$  a s v


Question 2


Solve

a) $3(x-1)^2=0$  a s v
b) $5(x-11)^2=0$  a s v
c) $\frac14(x+9)^2=0$  a s v
d) $9(x+2.3)^2=0$  a s v
e) $(2x-8)^2=0$  a s v
f) $\frac37(4x+11)^2=0$  a s v


Question 3


Solve, by taking out a common factor

a) $2x^2+16x+32=0$  a s v
b) $3x^2+42x+147=0$  a s v
c) $5x^2-30x+45=0$  a s v
d) $\frac12x^2-6x+18=0$  a s v
e) $x^3+2x^2+x=0$  a s v
f) $0.1x^4-2x^3+x^2=0$  a s v


Question 4


Solve. Remember there are two solutions

a) $2(x-1)^2=50$  a s v
b) $3(x-2)^2=12$  a s v
c) $8(x+8)^2=800$  a s v
d) $0.8(x+1)^2=51.2$  a s v
e) $\frac14(x+15)^2=36$  a s v
f) $\frac37(x-54)^2=21$  a s v


Question 5


Solve by completing the square on the left hand side

a) $2x^2+12x+18=32$  a s v
b) $4x^2-40x+100=16$  a s v
c) $\frac12x^2-8x+32=50$  a s v
d) $4x^2-80x+400=1$  a s v
e) $x^2+2x+1=0.36$  a s v
f) $0.8x^2-9.6x+28.8=5$  a s v


Question 6


Solve by completing the square

a) $2x^2+4x-48=0$  a s v
b) $3x^2+30x+72=0$  a s v
c) $5x^2-20x=0$  a s v
d) $4x^2-56x+160=0$  a s v
e) $7x^2+42x-189=0$  a s v
f) $9x^2-126x-288=0$  a s v


Question 7


Solve by completing the square

a) $2x^2-12x+\frac{35}{2}=0$  a s v
b) $3x^2-6x+\frac83=0$  a s v
c) $2x^2+12x+17\frac79=0$  a s v
d) $4x^2-24x+\frac{224}{9}=0$  a s v
e) $5x^2+50x+124\frac{19}{20}=0$  a s v
f) $8x^2-48x+60\frac{12}{25}=0$  a s v


Question 8


Solve

a) $3\left(x+\frac12\right)^2=\frac34$  a s v
b) $5\left(x-\frac25\right)^2=\frac15$  a s v
c) $2\left(x+\frac14\right)^2=1\frac{1}{8}$  a s v
d) $8\left(x-\frac67\right)^2=\frac{32}{49}$  a s v
e) $\frac12\left(x+3.5\right)^2=\frac{25}{8}$  a s v
f) $\frac37\left(x-1\frac16\right)^2=\frac{27}{28}$  a s v


Question 9


Solve by completing the square on the left hand side

a) $2x^2-2x+\frac12=2$  a s v
b) $5x^2+2x+\frac15=20$  a s v
c) $9x^2-12x+4=81$  a s v
d) $\frac12x^2+4x+8=8$  a s v
e) $\frac13x^2-\frac13x+\frac{1}{12}=27$  a s v
f) $112x^2-168x+63=448$  a s v


Question 10


Solve by completing the square

a) $8x^2-8x-70=0$  a s v
b) $4x^2+20x+21=0$  a s v
c) $20x^2-60x-35=0$  a s v
d) $2x^2+2x-\frac{35}{2}=0$  a s v
e) $3x^2-9x-\frac{21}{4}=0$  a s v
f) $\frac12x^2+\frac54x-\frac{119}{32}=0$  a s v