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Simplifying 96 = x2 + 12x Reorder the terms: 96 = 12x + x2 Solving 96 = 12x + x2 Solving for variable 'x'. Reorder the terms: 96 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 96 + -12x + -1x2 = 0 + x2 + -1x2 96 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 96 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -96 + 12x + x2 = 0 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.Subproblem 1
x + 6 = 11.489125293 Simplifying x + 6 = 11.489125293 Reorder the terms: 6 + x = 11.489125293 Solving 6 + x = 11.489125293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 11.489125293 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.489125293 + -6 x = 11.489125293 + -6 Combine like terms: 11.489125293 + -6 = 5.489125293 x = 5.489125293 Simplifying x = 5.489125293Subproblem 2
x + 6 = -11.489125293 Simplifying x + 6 = -11.489125293 Reorder the terms: 6 + x = -11.489125293 Solving 6 + x = -11.489125293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -11.489125293 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.489125293 + -6 x = -11.489125293 + -6 Combine like terms: -11.489125293 + -6 = -17.489125293 x = -17.489125293 Simplifying x = -17.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.489125293, -17.489125293}
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