Solving Quadratic Equations

Zero Product

100

Solve (x - 7)(x + 2) = 0

x₁ = 7 ,  x₂ = -2

200

Solve (2x - 7)(6x + 9) = 0

x₁ = 3.5 , x₂ = -1.5

300

Simplify ( x² + x - 2 ) / ( x² + 2x - 3 ) .

(x +2) / (x+3)

400

Simplify ( x² + x - 20 ) / ( x² + 8x + 15 ) .

(x - 4) / (x+3)

500

Simplify ( 2x² + x - 3 ) / ( 2x² + 13x + 15 ) .

(x - 1) / (x+5)

Higher Degree

100

x⁴  = 81

x₁ = 3 x₂ = -3 

200

 x⁴ - 10 x²+ 9 = 0

x₁ = 3 x₂ = -3 x₃ = 1 x₄ = -1

300

x⁶ + 7x³ - 8 = 0

x₁ = 1 ,  x₂ = -2

400

x⁸ - 17x^4 + 16 = 0

x₁ = 1 ,  x₂ = -1 , x₃ =2 , x₄ =-2

500

x¹⁰ + 31x⁵  - 32 = 0

x₁ = 1 x₂ = -2

Quadratic Formula

100

Solve x² - 7x = 0 .

x₁ = 0 , x₂ = 7

200

Solve  x² + 6x + 5 = 0 .

x = -1 x = -5

300

Solve (x+5)(x + 2)  = 10 .

x₁ = 0 , x₂ = -7

400

Solve  (x + 2)(2x -3 )+x - 4 = -6

x₁ = -2 , x₂ = 1

500

Solve  (2x - 3)(x + 8 ) + (5x - 3)(2x + 7) = -36x + 99

x₁ = -8 , x₂ = 1.5