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Simplifying 0 = x2 + 12x + -40 Reorder the terms: 0 = -40 + 12x + x2 Solving 0 = -40 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + 40 = 40 40 + -12x + -1x2 = -40 + 12x + x2 + 40 + -12x + -1x2 Reorder the terms: 40 + -12x + -1x2 = -40 + 40 + 12x + -12x + x2 + -1x2 Combine like terms: -40 + 40 = 0 40 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 40 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 40 + -12x + -1x2 = 0 + x2 + -1x2 40 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 12x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 12x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 12x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 12x + x2 = 0 + 40 12x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 12x + x2 = 40 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 = 40 + 36 Reorder the terms: 36 + 12x + x2 = 40 + 36 Combine like terms: 40 + 36 = 76 36 + 12x + x2 = 76 Factor a perfect square on the left side: (x + 6)(x + 6) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + 6) equal to 8.717797887 and -8.717797887.Subproblem 1
x + 6 = 8.717797887 Simplifying x + 6 = 8.717797887 Reorder the terms: 6 + x = 8.717797887 Solving 6 + x = 8.717797887 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 = 8.717797887 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.717797887 + -6 x = 8.717797887 + -6 Combine like terms: 8.717797887 + -6 = 2.717797887 x = 2.717797887 Simplifying x = 2.717797887Subproblem 2
x + 6 = -8.717797887 Simplifying x + 6 = -8.717797887 Reorder the terms: 6 + x = -8.717797887 Solving 6 + x = -8.717797887 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 = -8.717797887 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.717797887 + -6 x = -8.717797887 + -6 Combine like terms: -8.717797887 + -6 = -14.717797887 x = -14.717797887 Simplifying x = -14.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.717797887, -14.717797887}
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