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Simplifying 0 = -128 + 18x + x2 Solving 0 = -128 + 18x + x2 Solving for variable 'x'. Combine like terms: 0 + 128 = 128 128 + -18x + -1x2 = -128 + 18x + x2 + 128 + -18x + -1x2 Reorder the terms: 128 + -18x + -1x2 = -128 + 128 + 18x + -18x + x2 + -1x2 Combine like terms: -128 + 128 = 0 128 + -18x + -1x2 = 0 + 18x + -18x + x2 + -1x2 128 + -18x + -1x2 = 18x + -18x + x2 + -1x2 Combine like terms: 18x + -18x = 0 128 + -18x + -1x2 = 0 + x2 + -1x2 128 + -18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 128 + -18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -128 + 18x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + 18x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 18x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 18x + x2 = 0 + 128 18x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 18x + x2 = 128 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 128 + 81 Reorder the terms: 81 + 18x + x2 = 128 + 81 Combine like terms: 128 + 81 = 209 81 + 18x + x2 = 209 Factor a perfect square on the left side: (x + 9)(x + 9) = 209 Calculate the square root of the right side: 14.456832295 Break this problem into two subproblems by setting (x + 9) equal to 14.456832295 and -14.456832295.Subproblem 1
x + 9 = 14.456832295 Simplifying x + 9 = 14.456832295 Reorder the terms: 9 + x = 14.456832295 Solving 9 + x = 14.456832295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 14.456832295 + -9 Combine like terms: 9 + -9 = 0 0 + x = 14.456832295 + -9 x = 14.456832295 + -9 Combine like terms: 14.456832295 + -9 = 5.456832295 x = 5.456832295 Simplifying x = 5.456832295Subproblem 2
x + 9 = -14.456832295 Simplifying x + 9 = -14.456832295 Reorder the terms: 9 + x = -14.456832295 Solving 9 + x = -14.456832295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -14.456832295 + -9 Combine like terms: 9 + -9 = 0 0 + x = -14.456832295 + -9 x = -14.456832295 + -9 Combine like terms: -14.456832295 + -9 = -23.456832295 x = -23.456832295 Simplifying x = -23.456832295Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.456832295, -23.456832295}
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