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Simplifying 6x = 129.6 + -1x2 Solving 6x = 129.6 + -1x2 Solving for variable 'x'. Reorder the terms: -129.6 + 6x + x2 = 129.6 + -1x2 + -129.6 + x2 Reorder the terms: -129.6 + 6x + x2 = 129.6 + -129.6 + -1x2 + x2 Combine like terms: 129.6 + -129.6 = 0.0 -129.6 + 6x + x2 = 0.0 + -1x2 + x2 -129.6 + 6x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -129.6 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '129.6' to each side of the equation. -129.6 + 6x + 129.6 + x2 = 0 + 129.6 Reorder the terms: -129.6 + 129.6 + 6x + x2 = 0 + 129.6 Combine like terms: -129.6 + 129.6 = 0.0 0.0 + 6x + x2 = 0 + 129.6 6x + x2 = 0 + 129.6 Combine like terms: 0 + 129.6 = 129.6 6x + x2 = 129.6 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 = 129.6 + 9 Reorder the terms: 9 + 6x + x2 = 129.6 + 9 Combine like terms: 129.6 + 9 = 138.6 9 + 6x + x2 = 138.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 138.6 Calculate the square root of the right side: 11.772850122 Break this problem into two subproblems by setting (x + 3) equal to 11.772850122 and -11.772850122.Subproblem 1
x + 3 = 11.772850122 Simplifying x + 3 = 11.772850122 Reorder the terms: 3 + x = 11.772850122 Solving 3 + x = 11.772850122 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 = 11.772850122 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.772850122 + -3 x = 11.772850122 + -3 Combine like terms: 11.772850122 + -3 = 8.772850122 x = 8.772850122 Simplifying x = 8.772850122Subproblem 2
x + 3 = -11.772850122 Simplifying x + 3 = -11.772850122 Reorder the terms: 3 + x = -11.772850122 Solving 3 + x = -11.772850122 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 = -11.772850122 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.772850122 + -3 x = -11.772850122 + -3 Combine like terms: -11.772850122 + -3 = -14.772850122 x = -14.772850122 Simplifying x = -14.772850122Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.772850122, -14.772850122}
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