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Simplifying x2 + -7x + -39 = 0 Reorder the terms: -39 + -7x + x2 = 0 Solving -39 + -7x + 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 + -7x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -7x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -7x + x2 = 0 + 39 -7x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -7x + x2 = 39 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 39 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 39 + 12.25 Combine like terms: 39 + 12.25 = 51.25 12.25 + -7x + x2 = 51.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -3.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -3.5 = 7.158910532 Simplifying x + -3.5 = 7.158910532 Reorder the terms: -3.5 + x = 7.158910532 Solving -3.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 7.158910532 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 7.158910532 + 3.5 x = 7.158910532 + 3.5 Combine like terms: 7.158910532 + 3.5 = 10.658910532 x = 10.658910532 Simplifying x = 10.658910532Subproblem 2
x + -3.5 = -7.158910532 Simplifying x + -3.5 = -7.158910532 Reorder the terms: -3.5 + x = -7.158910532 Solving -3.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -7.158910532 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -7.158910532 + 3.5 x = -7.158910532 + 3.5 Combine like terms: -7.158910532 + 3.5 = -3.658910532 x = -3.658910532 Simplifying x = -3.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.658910532, -3.658910532}
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