Answer:
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.
