Solve the equation by first factoring the quadratic expression.
1. x2+4.5x=0 2. x2-9x=0 3. -x2+10x=0
1.
x ^ 2 + 4.5 x = 0
x ^ 2 + 9 x / 2 = 0
x / 2 ( 2 x + 9 ) = 0 Multiply both sides by 2
x ( 2 x + 9 ) = 0
First solution:
obviously x = 0
Second solution:
2 x + 9 = 0 Subtract 9 to both sides
2 x + 9 - 9 = 0 - 9
2 x = - 9 Divide both sides by 2
x = - 9 / 2
Solutions are x = 0 and x = - 9 / 2
2.
x ^ 2 - 9 x = 0
x ( x - 9 ) = 0
First solution:
obviously x = 0
Second solution:
x - 9 = 0 Add 9 to both sides
x - 9 + 9 = 0 + 9
x = 9
Solutions are x = 0 and x = 9
3.
- x ^ 2 + 10 x = 0
x ( - x + 10 ) = 0
First solution:
obviously x = 0
Second solution:
- x + 10 = 0 Subtract 10 to both sides
- x + 10 - 10 = 0 - 10
- x = - 10 Multiply both sides by - 1
x = 10
Solutions are x = 0 and x = 10