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Simplifying 18x + x2 = 115.2 Solving 18x + x2 = 115.2 Solving for variable 'x'. Reorder the terms: -115.2 + 18x + x2 = 115.2 + -115.2 Combine like terms: 115.2 + -115.2 = 0.0 -115.2 + 18x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '115.2' to each side of the equation. -115.2 + 18x + 115.2 + x2 = 0.0 + 115.2 Reorder the terms: -115.2 + 115.2 + 18x + x2 = 0.0 + 115.2 Combine like terms: -115.2 + 115.2 = 0.0 0.0 + 18x + x2 = 0.0 + 115.2 18x + x2 = 0.0 + 115.2 Combine like terms: 0.0 + 115.2 = 115.2 18x + x2 = 115.2 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 = 115.2 + 81 Reorder the terms: 81 + 18x + x2 = 115.2 + 81 Combine like terms: 115.2 + 81 = 196.2 81 + 18x + x2 = 196.2 Factor a perfect square on the left side: (x + 9)(x + 9) = 196.2 Calculate the square root of the right side: 14.007141036 Break this problem into two subproblems by setting (x + 9) equal to 14.007141036 and -14.007141036.Subproblem 1
x + 9 = 14.007141036 Simplifying x + 9 = 14.007141036 Reorder the terms: 9 + x = 14.007141036 Solving 9 + x = 14.007141036 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 = 14.007141036 + -9 Combine like terms: 9 + -9 = 0 0 + x = 14.007141036 + -9 x = 14.007141036 + -9 Combine like terms: 14.007141036 + -9 = 5.007141036 x = 5.007141036 Simplifying x = 5.007141036Subproblem 2
x + 9 = -14.007141036 Simplifying x + 9 = -14.007141036 Reorder the terms: 9 + x = -14.007141036 Solving 9 + x = -14.007141036 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 = -14.007141036 + -9 Combine like terms: 9 + -9 = 0 0 + x = -14.007141036 + -9 x = -14.007141036 + -9 Combine like terms: -14.007141036 + -9 = -23.007141036 x = -23.007141036 Simplifying x = -23.007141036Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.007141036, -23.007141036}
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