SOLVING QUADRATIC EQUATIONS NOT WRITTEN IN STANDARD FORM

Use the quadratic formula to solve exactly for x :

Problem 1 :

(x + 2) (x - 1) = 2 - 3x

Solution :

(x + 2) (x - 1) = 2 - 3x

x²  - x + 2x - 2 = 2 - 3x

x² + x - 2 = 2 - 3x

Subtract 2 - 3x on each sides.

x² + x - 2 - 2 + 3x = 0

x² + 4x - 4 = 0

Using quadratic formula.

Problem 2 :

(2x + 1)² = 3 - x 

Solution :

(2x + 1)² = 3 - x 

(2x)² + 2(2x)(1) + 1² = 3 - x

4x² + 4x + 1 = 3 - x

Subtract 3 - x on each sides.

4x² + 4x + 1 - 3 + x  = 0

4x² + 5x - 2 = 0

Using quadratic formula.

Problem 3 :

(x - 2)² = 1 + x 

Solution :

(x - 2)² = 1 + x 

x² - 2(x)(2) + 2² = 1 + x

x² - 4x + 4 = 1 + x

Subtract 1 + x on each sides.

x² - 4x + 4 - 1 - x  = 0

x² - 5x + 3 = 0

Using quadratic formula.

Problem 4 :

Solution :

Using cross multiplication.

x - 1 = (2x + 1) (2 - x)

x - 1 = 4x - 2x² + 2 - x

x - 1 = 3x - 2x² + 2 

Subtract 3x - 2x² + 2 on each sides.

x - 1 - 3x + 2x² - 2 = 0

2x² - 2x - 3 = 0

Using quadratic formula.

Problem 5 :

Solution :

Using cross multiplication.

Using quadratic formula.

Problem 6 :

Solution :

Using cross multiplication.

Using quadratic formula.