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Simplifying -1x2 + -12x + -29 = 0 Reorder the terms: -29 + -12x + -1x2 = 0 Solving -29 + -12x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(29 + 12x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(29 + 12x + x2)' equal to zero and attempt to solve: Simplifying 29 + 12x + x2 = 0 Solving 29 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 12x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 12x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 12x + x2 = 0 + -29 12x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 12x + x2 = -29 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 = -29 + 36 Reorder the terms: 36 + 12x + x2 = -29 + 36 Combine like terms: -29 + 36 = 7 36 + 12x + x2 = 7 Factor a perfect square on the left side: (x + 6)(x + 6) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 6) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 6 = 2.645751311 Simplifying x + 6 = 2.645751311 Reorder the terms: 6 + x = 2.645751311 Solving 6 + x = 2.645751311 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 = 2.645751311 + -6 Combine like terms: 6 + -6 = 0 0 + x = 2.645751311 + -6 x = 2.645751311 + -6 Combine like terms: 2.645751311 + -6 = -3.354248689 x = -3.354248689 Simplifying x = -3.354248689Subproblem 2
x + 6 = -2.645751311 Simplifying x + 6 = -2.645751311 Reorder the terms: 6 + x = -2.645751311 Solving 6 + x = -2.645751311 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 = -2.645751311 + -6 Combine like terms: 6 + -6 = 0 0 + x = -2.645751311 + -6 x = -2.645751311 + -6 Combine like terms: -2.645751311 + -6 = -8.645751311 x = -8.645751311 Simplifying x = -8.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.354248689, -8.645751311}Solution
x = {-3.354248689, -8.645751311}
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