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Simplifying x2 + -31x + -16 = 0 Reorder the terms: -16 + -31x + x2 = 0 Solving -16 + -31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -31x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -31x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -31x + x2 = 0 + 16 -31x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -31x + x2 = 16 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = 16 + 240.25 Reorder the terms: 240.25 + -31x + x2 = 16 + 240.25 Combine like terms: 16 + 240.25 = 256.25 240.25 + -31x + x2 = 256.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (x + -15.5) equal to 16.007810594 and -16.007810594.Subproblem 1
x + -15.5 = 16.007810594 Simplifying x + -15.5 = 16.007810594 Reorder the terms: -15.5 + x = 16.007810594 Solving -15.5 + x = 16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 16.007810594 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 16.007810594 + 15.5 x = 16.007810594 + 15.5 Combine like terms: 16.007810594 + 15.5 = 31.507810594 x = 31.507810594 Simplifying x = 31.507810594Subproblem 2
x + -15.5 = -16.007810594 Simplifying x + -15.5 = -16.007810594 Reorder the terms: -15.5 + x = -16.007810594 Solving -15.5 + x = -16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -16.007810594 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -16.007810594 + 15.5 x = -16.007810594 + 15.5 Combine like terms: -16.007810594 + 15.5 = -0.507810594 x = -0.507810594 Simplifying x = -0.507810594Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.507810594, -0.507810594}
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