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Simplifying x2 + x + -12 = 39 Reorder the terms: -12 + x + x2 = 39 Solving -12 + x + x2 = 39 Solving for variable 'x'. Reorder the terms: -12 + -39 + x + x2 = 39 + -39 Combine like terms: -12 + -39 = -51 -51 + x + x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -51 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + x + x2 = 0 + 51 x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 x + x2 = 51 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 51 + 0.25 Reorder the terms: 0.25 + x + x2 = 51 + 0.25 Combine like terms: 51 + 0.25 = 51.25 0.25 + x + x2 = 51.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 0.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 0.5 = 7.158910532 Simplifying x + 0.5 = 7.158910532 Reorder the terms: 0.5 + x = 7.158910532 Solving 0.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.158910532 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.158910532 + -0.5 x = 7.158910532 + -0.5 Combine like terms: 7.158910532 + -0.5 = 6.658910532 x = 6.658910532 Simplifying x = 6.658910532Subproblem 2
x + 0.5 = -7.158910532 Simplifying x + 0.5 = -7.158910532 Reorder the terms: 0.5 + x = -7.158910532 Solving 0.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.158910532 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.158910532 + -0.5 x = -7.158910532 + -0.5 Combine like terms: -7.158910532 + -0.5 = -7.658910532 x = -7.658910532 Simplifying x = -7.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.658910532, -7.658910532}
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