Question

Solve the equation by first factoring the quadratic expression.

1. x2+4.5x=0 2. x2-9x=0 3. -x2+10x=0

Answer 1

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