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Simplifying 12x = x2 + -34 Reorder the terms: 12x = -34 + x2 Solving 12x = -34 + x2 Solving for variable 'x'. Reorder the terms: 34 + 12x + -1x2 = -34 + x2 + 34 + -1x2 Reorder the terms: 34 + 12x + -1x2 = -34 + 34 + x2 + -1x2 Combine like terms: -34 + 34 = 0 34 + 12x + -1x2 = 0 + x2 + -1x2 34 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 34 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -34 + -12x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + -12x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -12x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -12x + x2 = 0 + 34 -12x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -12x + x2 = 34 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 = 34 + 36 Reorder the terms: 36 + -12x + x2 = 34 + 36 Combine like terms: 34 + 36 = 70 36 + -12x + x2 = 70 Factor a perfect square on the left side: (x + -6)(x + -6) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + -6) equal to 8.366600265 and -8.366600265.Subproblem 1
x + -6 = 8.366600265 Simplifying x + -6 = 8.366600265 Reorder the terms: -6 + x = 8.366600265 Solving -6 + x = 8.366600265 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 = 8.366600265 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.366600265 + 6 x = 8.366600265 + 6 Combine like terms: 8.366600265 + 6 = 14.366600265 x = 14.366600265 Simplifying x = 14.366600265Subproblem 2
x + -6 = -8.366600265 Simplifying x + -6 = -8.366600265 Reorder the terms: -6 + x = -8.366600265 Solving -6 + x = -8.366600265 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 = -8.366600265 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.366600265 + 6 x = -8.366600265 + 6 Combine like terms: -8.366600265 + 6 = -2.366600265 x = -2.366600265 Simplifying x = -2.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.366600265, -2.366600265}
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