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Simplifying x2 + 26x + 83 = 0 Reorder the terms: 83 + 26x + x2 = 0 Solving 83 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-83' to each side of the equation. 83 + 26x + -83 + x2 = 0 + -83 Reorder the terms: 83 + -83 + 26x + x2 = 0 + -83 Combine like terms: 83 + -83 = 0 0 + 26x + x2 = 0 + -83 26x + x2 = 0 + -83 Combine like terms: 0 + -83 = -83 26x + x2 = -83 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -83 + 169 Reorder the terms: 169 + 26x + x2 = -83 + 169 Combine like terms: -83 + 169 = 86 169 + 26x + x2 = 86 Factor a perfect square on the left side: (x + 13)(x + 13) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 13) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 13 = 9.273618495 Simplifying x + 13 = 9.273618495 Reorder the terms: 13 + x = 9.273618495 Solving 13 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 9.273618495 + -13 Combine like terms: 13 + -13 = 0 0 + x = 9.273618495 + -13 x = 9.273618495 + -13 Combine like terms: 9.273618495 + -13 = -3.726381505 x = -3.726381505 Simplifying x = -3.726381505Subproblem 2
x + 13 = -9.273618495 Simplifying x + 13 = -9.273618495 Reorder the terms: 13 + x = -9.273618495 Solving 13 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -9.273618495 + -13 Combine like terms: 13 + -13 = 0 0 + x = -9.273618495 + -13 x = -9.273618495 + -13 Combine like terms: -9.273618495 + -13 = -22.273618495 x = -22.273618495 Simplifying x = -22.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.726381505, -22.273618495}
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