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Simplifying x2 + -18x + 16 = 144 Reorder the terms: 16 + -18x + x2 = 144 Solving 16 + -18x + x2 = 144 Solving for variable 'x'. Reorder the terms: 16 + -144 + -18x + x2 = 144 + -144 Combine like terms: 16 + -144 = -128 -128 + -18x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -128 + -18x + x2 = 0 Begin completing the square. 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 = 23.456832295 x = 23.456832295 Simplifying x = 23.456832295Subproblem 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 = -5.456832295 x = -5.456832295 Simplifying x = -5.456832295Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.456832295, -5.456832295}
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