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Simplifying 2x2 + 12x + -122 = 0 Reorder the terms: -122 + 12x + 2x2 = 0 Solving -122 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-61 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-61 + 6x + x2)' equal to zero and attempt to solve: Simplifying -61 + 6x + x2 = 0 Solving -61 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 6x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 6x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 6x + x2 = 0 + 61 6x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 6x + x2 = 61 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 61 + 9 Reorder the terms: 9 + 6x + x2 = 61 + 9 Combine like terms: 61 + 9 = 70 9 + 6x + x2 = 70 Factor a perfect square on the left side: (x + 3)(x + 3) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + 3) equal to 8.366600265 and -8.366600265.Subproblem 1
x + 3 = 8.366600265 Simplifying x + 3 = 8.366600265 Reorder the terms: 3 + x = 8.366600265 Solving 3 + x = 8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.366600265 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.366600265 + -3 x = 8.366600265 + -3 Combine like terms: 8.366600265 + -3 = 5.366600265 x = 5.366600265 Simplifying x = 5.366600265Subproblem 2
x + 3 = -8.366600265 Simplifying x + 3 = -8.366600265 Reorder the terms: 3 + x = -8.366600265 Solving 3 + x = -8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.366600265 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.366600265 + -3 x = -8.366600265 + -3 Combine like terms: -8.366600265 + -3 = -11.366600265 x = -11.366600265 Simplifying x = -11.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.366600265, -11.366600265}Solution
x = {5.366600265, -11.366600265}
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