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Simplifying 85 = x(x + -2) Reorder the terms: 85 = x(-2 + x) 85 = (-2 * x + x * x) 85 = (-2x + x2) Solving 85 = -2x + x2 Solving for variable 'x'. Reorder the terms: 85 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 85 + 2x + -1x2 = 0 + x2 + -1x2 85 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 85 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -85 + -2x + x2 = 0 Move the constant term to the right: Add '85' to each side of the equation. -85 + -2x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + -2x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -2x + x2 = 0 + 85 -2x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 -2x + x2 = 85 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 85 + 1 Reorder the terms: 1 + -2x + x2 = 85 + 1 Combine like terms: 85 + 1 = 86 1 + -2x + x2 = 86 Factor a perfect square on the left side: (x + -1)(x + -1) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + -1) equal to 9.273618495 and -9.273618495.Subproblem 1
x + -1 = 9.273618495 Simplifying x + -1 = 9.273618495 Reorder the terms: -1 + x = 9.273618495 Solving -1 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.273618495 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.273618495 + 1 x = 9.273618495 + 1 Combine like terms: 9.273618495 + 1 = 10.273618495 x = 10.273618495 Simplifying x = 10.273618495Subproblem 2
x + -1 = -9.273618495 Simplifying x + -1 = -9.273618495 Reorder the terms: -1 + x = -9.273618495 Solving -1 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.273618495 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.273618495 + 1 x = -9.273618495 + 1 Combine like terms: -9.273618495 + 1 = -8.273618495 x = -8.273618495 Simplifying x = -8.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.273618495, -8.273618495}
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