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Simplifying (x) = x2 + -18x + 86 x = x2 + -18x + 86 Reorder the terms: x = 86 + -18x + x2 Solving x = 86 + -18x + x2 Solving for variable 'x'. Reorder the terms: -86 + x + 18x + -1x2 = 86 + -18x + x2 + -86 + 18x + -1x2 Combine like terms: x + 18x = 19x -86 + 19x + -1x2 = 86 + -18x + x2 + -86 + 18x + -1x2 Reorder the terms: -86 + 19x + -1x2 = 86 + -86 + -18x + 18x + x2 + -1x2 Combine like terms: 86 + -86 = 0 -86 + 19x + -1x2 = 0 + -18x + 18x + x2 + -1x2 -86 + 19x + -1x2 = -18x + 18x + x2 + -1x2 Combine like terms: -18x + 18x = 0 -86 + 19x + -1x2 = 0 + x2 + -1x2 -86 + 19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -86 + 19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 86 + -19x + x2 = 0 Move the constant term to the right: Add '-86' to each side of the equation. 86 + -19x + -86 + x2 = 0 + -86 Reorder the terms: 86 + -86 + -19x + x2 = 0 + -86 Combine like terms: 86 + -86 = 0 0 + -19x + x2 = 0 + -86 -19x + x2 = 0 + -86 Combine like terms: 0 + -86 = -86 -19x + x2 = -86 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -86 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -86 + 90.25 Combine like terms: -86 + 90.25 = 4.25 90.25 + -19x + x2 = 4.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -9.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -9.5 = 2.061552813 Simplifying x + -9.5 = 2.061552813 Reorder the terms: -9.5 + x = 2.061552813 Solving -9.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 2.061552813 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 2.061552813 + 9.5 x = 2.061552813 + 9.5 Combine like terms: 2.061552813 + 9.5 = 11.561552813 x = 11.561552813 Simplifying x = 11.561552813Subproblem 2
x + -9.5 = -2.061552813 Simplifying x + -9.5 = -2.061552813 Reorder the terms: -9.5 + x = -2.061552813 Solving -9.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -2.061552813 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -2.061552813 + 9.5 x = -2.061552813 + 9.5 Combine like terms: -2.061552813 + 9.5 = 7.438447187 x = 7.438447187 Simplifying x = 7.438447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.561552813, 7.438447187}
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