Question

How do I solve the following quadratic equations step by step? 

1) y^2 - 5y - 24 = 0 

2) 4x^2 - 36 = 0 

3) 8x^2 + 10x + 3 = 0

Answer 1

1). y^2 - 5y - 24 = 0.

By factor by grouping.

y^2 - 8y + 3y - 24 = 0

y(y - 8) + 3(y - 8) = 0

Factor : (y - 8)(y + 3) = 0

Apply zero product property.

y - 8 = 0 and y + 3 = 0

y = 8 and y = - 3.

Solutions of the quadratic equation are y = 8 and y = - 3.

2). 4x^2 - 36 = 0.

4x^2 = 36

x^2 = 36/4 = 9

x^2 = ( ± 3 )^2

Extract square roots from each side.

x = ± 3.

Solution of the quadratic equation are x = 3 and x = - 3.

3). 8x^2 + 10x + 3 = 0.

By factor by grouping.

8x^2 + 6x + 4x + 3 = 0

2x(4x + 3) + 1(4x + 3) = 0

Factor : (4x + 3)(2x + 1) = 0

Apply zero product property.

4x + 3 = 0 and 2x + 1 = 0

x = - 3/4 and x = - 1/2.

Solutions of the quadratic equation are x = - 3/4 and x = - 1/2.