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Simplifying 34.5 = 12x + -1x2 Solving 34.5 = 12x + -1x2 Solving for variable 'x'. Reorder the terms: 34.5 + -12x + x2 = 12x + -12x + -1x2 + x2 Combine like terms: 12x + -12x = 0 34.5 + -12x + x2 = 0 + -1x2 + x2 34.5 + -12x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 34.5 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34.5' to each side of the equation. 34.5 + -12x + -34.5 + x2 = 0 + -34.5 Reorder the terms: 34.5 + -34.5 + -12x + x2 = 0 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + -12x + x2 = 0 + -34.5 -12x + x2 = 0 + -34.5 Combine like terms: 0 + -34.5 = -34.5 -12x + x2 = -34.5 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 = -34.5 + 36 Reorder the terms: 36 + -12x + x2 = -34.5 + 36 Combine like terms: -34.5 + 36 = 1.5 36 + -12x + x2 = 1.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -6) equal to 1.224744871 and -1.224744871.Subproblem 1
x + -6 = 1.224744871 Simplifying x + -6 = 1.224744871 Reorder the terms: -6 + x = 1.224744871 Solving -6 + x = 1.224744871 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 = 1.224744871 + 6 Combine like terms: -6 + 6 = 0 0 + x = 1.224744871 + 6 x = 1.224744871 + 6 Combine like terms: 1.224744871 + 6 = 7.224744871 x = 7.224744871 Simplifying x = 7.224744871Subproblem 2
x + -6 = -1.224744871 Simplifying x + -6 = -1.224744871 Reorder the terms: -6 + x = -1.224744871 Solving -6 + x = -1.224744871 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 = -1.224744871 + 6 Combine like terms: -6 + 6 = 0 0 + x = -1.224744871 + 6 x = -1.224744871 + 6 Combine like terms: -1.224744871 + 6 = 4.775255129 x = 4.775255129 Simplifying x = 4.775255129Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.224744871, 4.775255129}
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