Create a list of steps, in order, that will solve the following equation. 1/2 (x+5) ^2+2=42.5

Roots are [4, - 14}.

Step-by-step explanation:

1/2 (x+5) ^2 + 2 = 42.5

Work out the square of the parentheses:

1/2 (x^2 + 10x + 25) + 2 = 42.5

Multiply the parentheses by 1/2:

1/2 x^2 + 5x + 12.5 + 2 = 42.5

Subtract 42.5 from both sides of the equation:

1 / 2x^2 + 5x + 14.5 - 42.5 = 0

Simplify:

1/2 x^2 + 5x - 28 = 0

Multiply through by 2 to get rid of the 1/2:

x^2 + 10x - 56 = 0

Factor:-

(x + 14) (x - 4) = 0

Either x + 14 = 0 giving x = - 14.

or x - 4 = 0 giving x = 4.