Factoring
x2 - 8x = 0
x(x-8)=0
x-8=0
x=0, x = 8
(X2 / 2) + 3 = 11
(X2 / 2) + 3 = 11
x2 / 2 = 8
X2 = 16
x= +/- 4
X2 + 14x = 15
(14/2)2 = 49
x2 + 14x + 49 = 15 + 49
(x+ 7)2 = 15 + 49
(x+7)2 = 64
x+7 = +/- 8
x = -7 +/- 8
x = 1
x = -15
2x2 + 2x - 12 = 0
2x2 + 2x - 12 = 0
a=2 b=2 c=-12
x=(-b +/- √(b2-4ac)) / 2a
x= (-2 +/- √(22 - 4(2)(-12))) / 2(2)
x= (-2 +/- √100) / 4
x = (-2 +/- 10) /4
x= 2 or x=-3
(x - 2) (x + 4)
2(x+3)2 = 40
(x+3)^2 = 20. Divide both sides by 2
X+3= +/- √20. square root both sides
x + 3 = +/- 2 √5. Break down sqrt 20
x= -3 +/- 2 √5 subtract 3 from boths ides
x2-8x = 9
x2- 8x +(-4)2=9 + 16 We get -4 and 16 from (-8/2)
(x-4)2=25
x-4= +/- 5
x= 4+/- 5
x= 9 x= -1
9x2 - 6x + 1 = 0
a=9 b=-6 c=1
x= (-b+/- √(b2- 4ac))/ 2a
x= (6 +/- √(36 - 4(9)(1))) / 2(9)
x= (6 +/- √0)/18
x= 6/18
x= 1/3. <----- simplified
2x2 - 6 = x
2x^2 - x - 6 = 0
2x^2 + 3x - 4x - 6 = 0
x(2x + 3) - 2(2x+3) = 0
(x-2)(2x+3) = 0
x - 2 = 0 2x+3 = 0
x= 2. x= -(3/2)
(x-2)2 / (-2) = 2
(x-2)2 = -4 multiplying both sides by -2
x-2 = +/- √-4. square root both sides
no solution since you cant have a negative number in a square root
2x2+10 = -16x
2x2+16x = -10
2x2+16x + _____ = -10 + ____
x2 + 8x + (4)2 = -5 + 16
(x+4)2 = 11
x+4 = +/- √11
x= -4 +/- √11
5x2+1 = -3x
5x2 + 3x + 1 = 0 subract 3x from both sides
a =5 b=3 c =1. identify each value
x= (-b+/- √(b2- 4ac))/ 2a
x= (-3+/- √((3)2 - 4(5)(1))) / 2(5)
x =( -3 +/- √-11 ) / 10
No real solution
2x2 - 9x - 35 = 0
(2x+5) (x-7)
5 = (x-2 / 3)2
+/- √5 = (x-2) / 3 square root both sides
+/- 3 √5 = x-2 multiply both sides by 3
x = 2 +/- 3 √5
X2 - 5x = 8
(-5/2)2 = 25/4
x2 - 5x + 25/4 = 8 + 25/4
(x - 5/2)2 = 8 + 25/4
(x-5/2)2 = 57/4
x - 5/2 = +/- sqrt (57/4)
x - 5/2 = +/- (sqrt 57) / 2
x = 5/2 +/- (sqrt 57) / 2
-3x2 = 4-6x
-3x2 + 6x - 4 = 0
a=-3 b=6 c=-4
x= (-b+/- √(b2- 4ac))/ 2a
x= (3 +/- √(36-4(-3)(-4))) / 2(-3)
x = (3 +/- √-12) / -6
No real solution
X3 - 25x = 25 - x2
x3 + x2 - 25x - 25 = 0
x2 (x+1) - 25(x+1) = 0
(x2 - 25)(x+1) = 0
(x+5)(x-5)(x+1) = 0
x+5 = 0 x -5 = 0. x+1 = 0
x=-5 x=5 x=-1
(x2 + 4)2 - 5 = 20
(x2 + 4)2 = 25 * add 5 to each side
x2 + 4 = 5 * take the square root of each side
x2 = 1 *subtract 4 from each side
x = +-1 * take the square root of each side
x2-4x = -2
(-4 x 1/2)2 = 4
x2-4x + 4 = -2 + 4
(x-2)2 = -2 + 4
(x-2)2 = 2
x-2 = +/- √2
x = 2 +/- √2
5x2 + 2 = 4x + 4
5x2 - 4x -2
a=5 b=-4 b=-2
x= (-b+/- √(b2- 4ac))/ 2a
x = (4+/- √(16 - 4(5)(-2))) / 2(5)
x = (4 +/- √56) / 10
x = (4 +/- 2 √14) /10
x = (4/10) +/- (2√14)/10
x= (2/5) +/- √(14)/5