solve: x² + 12x - 96=0
Answers
Simplifying
x2 + 12x + -96 = 0
Reorder the terms:
-96 + 12x + x2 = 0
Solving
-96 + 12x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '96' to each side of the equation.
-96 + 12x + 96 + x2 = 0 + 96
Reorder the terms:
-96 + 96 + 12x + x2 = 0 + 96
Combine like terms: -96 + 96 = 0
0 + 12x + x2 = 0 + 96
12x + x2 = 0 + 96
Combine like terms: 0 + 96 = 96
12x + x2 = 96
The x term is 12x. Take half its coefficient (6).
Square it (36) and add it to both sides.
Add '36' to each side of the equation.
12x + 36 + x2 = 96 + 36
Reorder the terms:
36 + 12x + x2 = 96 + 36
Combine like terms: 96 + 36 = 132
36 + 12x + x2 = 132
Factor a perfect square on the left side:
(x + 6)(x + 6) = 132
Calculate the square root of the right side: 11.489125293
Break this problem into two subproblems by setting
(x + 6) equal to 11.489125293 and -11.489125293.