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Simplifying x2 + -18x = 1.25 Reorder the terms: -18x + x2 = 1.25 Solving -18x + x2 = 1.25 Solving for variable 'x'. Reorder the terms: -1.25 + -18x + x2 = 1.25 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 -1.25 + -18x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -18x + 1.25 + x2 = 0.00 + 1.25 Reorder the terms: -1.25 + 1.25 + -18x + x2 = 0.00 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -18x + x2 = 0.00 + 1.25 -18x + x2 = 0.00 + 1.25 Combine like terms: 0.00 + 1.25 = 1.25 -18x + x2 = 1.25 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 = 1.25 + 81 Reorder the terms: 81 + -18x + x2 = 1.25 + 81 Combine like terms: 1.25 + 81 = 82.25 81 + -18x + x2 = 82.25 Factor a perfect square on the left side: (x + -9)(x + -9) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -9) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -9 = 9.069178574 Simplifying x + -9 = 9.069178574 Reorder the terms: -9 + x = 9.069178574 Solving -9 + x = 9.069178574 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 = 9.069178574 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.069178574 + 9 x = 9.069178574 + 9 Combine like terms: 9.069178574 + 9 = 18.069178574 x = 18.069178574 Simplifying x = 18.069178574Subproblem 2
x + -9 = -9.069178574 Simplifying x + -9 = -9.069178574 Reorder the terms: -9 + x = -9.069178574 Solving -9 + x = -9.069178574 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 = -9.069178574 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.069178574 + 9 x = -9.069178574 + 9 Combine like terms: -9.069178574 + 9 = -0.069178574 x = -0.069178574 Simplifying x = -0.069178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.069178574, -0.069178574}
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