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Simplifying -1x2 + -10x = -31 Reorder the terms: -10x + -1x2 = -31 Solving -10x + -1x2 = -31 Solving for variable 'x'. Reorder the terms: 31 + -10x + -1x2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + 10x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 10x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 10x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 10x + x2 = 0 + 31 10x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 10x + x2 = 31 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 31 + 25 Reorder the terms: 25 + 10x + x2 = 31 + 25 Combine like terms: 31 + 25 = 56 25 + 10x + x2 = 56 Factor a perfect square on the left side: (x + 5)(x + 5) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 5) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 5 = 7.483314774 Simplifying x + 5 = 7.483314774 Reorder the terms: 5 + x = 7.483314774 Solving 5 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.483314774 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.483314774 + -5 x = 7.483314774 + -5 Combine like terms: 7.483314774 + -5 = 2.483314774 x = 2.483314774 Simplifying x = 2.483314774Subproblem 2
x + 5 = -7.483314774 Simplifying x + 5 = -7.483314774 Reorder the terms: 5 + x = -7.483314774 Solving 5 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.483314774 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.483314774 + -5 x = -7.483314774 + -5 Combine like terms: -7.483314774 + -5 = -12.483314774 x = -12.483314774 Simplifying x = -12.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.483314774, -12.483314774}
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