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Simplifying x2 + -20x + 39 = 0 Reorder the terms: 39 + -20x + x2 = 0 Solving 39 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + -20x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + -20x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -20x + x2 = 0 + -39 -20x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 -20x + x2 = -39 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -39 + 100 Reorder the terms: 100 + -20x + x2 = -39 + 100 Combine like terms: -39 + 100 = 61 100 + -20x + x2 = 61 Factor a perfect square on the left side: (x + -10)(x + -10) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -10) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -10 = 7.810249676 Simplifying x + -10 = 7.810249676 Reorder the terms: -10 + x = 7.810249676 Solving -10 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 7.810249676 + 10 Combine like terms: -10 + 10 = 0 0 + x = 7.810249676 + 10 x = 7.810249676 + 10 Combine like terms: 7.810249676 + 10 = 17.810249676 x = 17.810249676 Simplifying x = 17.810249676Subproblem 2
x + -10 = -7.810249676 Simplifying x + -10 = -7.810249676 Reorder the terms: -10 + x = -7.810249676 Solving -10 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -7.810249676 + 10 Combine like terms: -10 + 10 = 0 0 + x = -7.810249676 + 10 x = -7.810249676 + 10 Combine like terms: -7.810249676 + 10 = 2.189750324 x = 2.189750324 Simplifying x = 2.189750324Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.810249676, 2.189750324}
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