Solving Using Square Roots
Use square roots to solve the quadratic equation
x2 + 12x + 36 = 25
x = -11 and x = -1
Rewrite
x^2+4x+3=0
in the form
(x-p)^2=q
(x+2)^2=1
Solve by completing the square
x^2+10x-1=0
x=-5+sqrt26
x=-5-sqrt26
Write the equation in vertex form
y=x^2-6x+4
y=(x-3)^2-5
Use square roots to solve the quadratic equation
x2 - 10x + 25 = 144
x = 17 and x = -7
Rewrite
x^2-6x+13=0
in the form
(x-p)^2=q
(x-3)^2=-4
Solve by completing the square
x^2+2x-7=0
x=-1+2sqrt2
x=-1-2sqrt2
Write the equation in vertex form
y=x^2+14x+50
y=(x+7)^2+1
Use square roots to solve the quadratic equation
x^2+6x+9=49/4
x = 1/2 , x = -13/2
Rewrite
0=x^2-18x+64
in the form
(x-p)^2=q
(x-9)^2=17
Solve by completing the square
-x^2+6x+10=0
x=3+sqrt19
x=3-sqrt19
Write the equation in vertex form
y=3x^2+8x+2
y=3(x+4/3)^2-10/3
Use square roots to solve the quadratic equation
x^2-22x+121=225
x = -4 , x = 26
Rewrite
0=4x^2+4x-14
in the form
(x-p)^2=q
(x+1/2)^2=15/4
Solve by completing the square
x^2+5x=3x+11
x=-1+2sqrt3
x=-1-2sqrt3
Write the equation in vertex form
y=-2x^2+6x-2
y=-2(x-3/2)^2+5/2
Use square roots to solve the quadratic equation
50=2x^2+16x+32
x = -9 , x = 1
Rewrite
x^2+0.6x-19.1=0
in the form
(x-p)^2=q
(x+0.3)^2=19.19
Solve by completing the square
5x^2-25=10x
x=1+sqrt6
x=1-sqrt6
Write the equation in vertex form
y=x^2-14x+71
y=(x-7)^2+22