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Simplifying x2 + -31x + -84 = 0 Reorder the terms: -84 + -31x + x2 = 0 Solving -84 + -31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -31x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -31x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -31x + x2 = 0 + 84 -31x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -31x + x2 = 84 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 = 84 + 240.25 Reorder the terms: 240.25 + -31x + x2 = 84 + 240.25 Combine like terms: 84 + 240.25 = 324.25 240.25 + -31x + x2 = 324.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 324.25 Calculate the square root of the right side: 18.006943105 Break this problem into two subproblems by setting (x + -15.5) equal to 18.006943105 and -18.006943105.Subproblem 1
x + -15.5 = 18.006943105 Simplifying x + -15.5 = 18.006943105 Reorder the terms: -15.5 + x = 18.006943105 Solving -15.5 + x = 18.006943105 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 = 18.006943105 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 18.006943105 + 15.5 x = 18.006943105 + 15.5 Combine like terms: 18.006943105 + 15.5 = 33.506943105 x = 33.506943105 Simplifying x = 33.506943105Subproblem 2
x + -15.5 = -18.006943105 Simplifying x + -15.5 = -18.006943105 Reorder the terms: -15.5 + x = -18.006943105 Solving -15.5 + x = -18.006943105 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 = -18.006943105 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -18.006943105 + 15.5 x = -18.006943105 + 15.5 Combine like terms: -18.006943105 + 15.5 = -2.506943105 x = -2.506943105 Simplifying x = -2.506943105Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.506943105, -2.506943105}
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