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Simplifying x2 + -18x + 20 = 0 Reorder the terms: 20 + -18x + x2 = 0 Solving 20 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -18x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -18x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -18x + x2 = 0 + -20 -18x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -18x + x2 = -20 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 = -20 + 81 Reorder the terms: 81 + -18x + x2 = -20 + 81 Combine like terms: -20 + 81 = 61 81 + -18x + x2 = 61 Factor a perfect square on the left side: (x + -9)(x + -9) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -9) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -9 = 7.810249676 Simplifying x + -9 = 7.810249676 Reorder the terms: -9 + x = 7.810249676 Solving -9 + x = 7.810249676 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 = 7.810249676 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.810249676 + 9 x = 7.810249676 + 9 Combine like terms: 7.810249676 + 9 = 16.810249676 x = 16.810249676 Simplifying x = 16.810249676Subproblem 2
x + -9 = -7.810249676 Simplifying x + -9 = -7.810249676 Reorder the terms: -9 + x = -7.810249676 Solving -9 + x = -7.810249676 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 = -7.810249676 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.810249676 + 9 x = -7.810249676 + 9 Combine like terms: -7.810249676 + 9 = 1.189750324 x = 1.189750324 Simplifying x = 1.189750324Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.810249676, 1.189750324}
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