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Simplifying x2 + -19x + 39 = 0 Reorder the terms: 39 + -19x + x2 = 0 Solving 39 + -19x + 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 + -19x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + -19x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -19x + x2 = 0 + -39 -19x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 -19x + x2 = -39 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -39 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -39 + 90.25 Combine like terms: -39 + 90.25 = 51.25 90.25 + -19x + x2 = 51.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -9.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -9.5 = 7.158910532 Simplifying x + -9.5 = 7.158910532 Reorder the terms: -9.5 + x = 7.158910532 Solving -9.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 7.158910532 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 7.158910532 + 9.5 x = 7.158910532 + 9.5 Combine like terms: 7.158910532 + 9.5 = 16.658910532 x = 16.658910532 Simplifying x = 16.658910532Subproblem 2
x + -9.5 = -7.158910532 Simplifying x + -9.5 = -7.158910532 Reorder the terms: -9.5 + x = -7.158910532 Solving -9.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -7.158910532 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -7.158910532 + 9.5 x = -7.158910532 + 9.5 Combine like terms: -7.158910532 + 9.5 = 2.341089468 x = 2.341089468 Simplifying x = 2.341089468Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.658910532, 2.341089468}
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