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Simplifying 15x + -1.86x2 + -25 = 0 Reorder the terms: -25 + 15x + -1.86x2 = 0 Solving -25 + 15x + -1.86x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.86 the coefficient of the squared term: Divide each side by '-1.86'. 13.44086022 + -8.064516129x + x2 = 0 Move the constant term to the right: Add '-13.44086022' to each side of the equation. 13.44086022 + -8.064516129x + -13.44086022 + x2 = 0 + -13.44086022 Reorder the terms: 13.44086022 + -13.44086022 + -8.064516129x + x2 = 0 + -13.44086022 Combine like terms: 13.44086022 + -13.44086022 = 0.00000000 0.00000000 + -8.064516129x + x2 = 0 + -13.44086022 -8.064516129x + x2 = 0 + -13.44086022 Combine like terms: 0 + -13.44086022 = -13.44086022 -8.064516129x + x2 = -13.44086022 The x term is -8.064516129x. Take half its coefficient (-4.032258065). Square it (16.25910510) and add it to both sides. Add '16.25910510' to each side of the equation. -8.064516129x + 16.25910510 + x2 = -13.44086022 + 16.25910510 Reorder the terms: 16.25910510 + -8.064516129x + x2 = -13.44086022 + 16.25910510 Combine like terms: -13.44086022 + 16.25910510 = 2.81824488 16.25910510 + -8.064516129x + x2 = 2.81824488 Factor a perfect square on the left side: (x + -4.032258065)(x + -4.032258065) = 2.81824488 Calculate the square root of the right side: 1.678762902 Break this problem into two subproblems by setting (x + -4.032258065) equal to 1.678762902 and -1.678762902.Subproblem 1
x + -4.032258065 = 1.678762902 Simplifying x + -4.032258065 = 1.678762902 Reorder the terms: -4.032258065 + x = 1.678762902 Solving -4.032258065 + x = 1.678762902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + x = 1.678762902 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + x = 1.678762902 + 4.032258065 x = 1.678762902 + 4.032258065 Combine like terms: 1.678762902 + 4.032258065 = 5.711020967 x = 5.711020967 Simplifying x = 5.711020967Subproblem 2
x + -4.032258065 = -1.678762902 Simplifying x + -4.032258065 = -1.678762902 Reorder the terms: -4.032258065 + x = -1.678762902 Solving -4.032258065 + x = -1.678762902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + x = -1.678762902 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + x = -1.678762902 + 4.032258065 x = -1.678762902 + 4.032258065 Combine like terms: -1.678762902 + 4.032258065 = 2.353495163 x = 2.353495163 Simplifying x = 2.353495163Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.711020967, 2.353495163}
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