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Simplifying 15x = 115 + -12x2 Solving 15x = 115 + -12x2 Solving for variable 'x'. Reorder the terms: -115 + 15x + 12x2 = 115 + -12x2 + -115 + 12x2 Reorder the terms: -115 + 15x + 12x2 = 115 + -115 + -12x2 + 12x2 Combine like terms: 115 + -115 = 0 -115 + 15x + 12x2 = 0 + -12x2 + 12x2 -115 + 15x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -115 + 15x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -9.583333333 + 1.25x + x2 = 0 Move the constant term to the right: Add '9.583333333' to each side of the equation. -9.583333333 + 1.25x + 9.583333333 + x2 = 0 + 9.583333333 Reorder the terms: -9.583333333 + 9.583333333 + 1.25x + x2 = 0 + 9.583333333 Combine like terms: -9.583333333 + 9.583333333 = 0.000000000 0.000000000 + 1.25x + x2 = 0 + 9.583333333 1.25x + x2 = 0 + 9.583333333 Combine like terms: 0 + 9.583333333 = 9.583333333 1.25x + x2 = 9.583333333 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 9.583333333 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 9.583333333 + 0.390625 Combine like terms: 9.583333333 + 0.390625 = 9.973958333 0.390625 + 1.25x + x2 = 9.973958333 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 9.973958333 Calculate the square root of the right side: 3.158157427 Break this problem into two subproblems by setting (x + 0.625) equal to 3.158157427 and -3.158157427.Subproblem 1
x + 0.625 = 3.158157427 Simplifying x + 0.625 = 3.158157427 Reorder the terms: 0.625 + x = 3.158157427 Solving 0.625 + x = 3.158157427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 3.158157427 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.158157427 + -0.625 x = 3.158157427 + -0.625 Combine like terms: 3.158157427 + -0.625 = 2.533157427 x = 2.533157427 Simplifying x = 2.533157427Subproblem 2
x + 0.625 = -3.158157427 Simplifying x + 0.625 = -3.158157427 Reorder the terms: 0.625 + x = -3.158157427 Solving 0.625 + x = -3.158157427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -3.158157427 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.158157427 + -0.625 x = -3.158157427 + -0.625 Combine like terms: -3.158157427 + -0.625 = -3.783157427 x = -3.783157427 Simplifying x = -3.783157427Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.533157427, -3.783157427}
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