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Simplifying x2 + 26x + 17 = 0 Reorder the terms: 17 + 26x + x2 = 0 Solving 17 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 26x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 26x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 26x + x2 = 0 + -17 26x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 26x + x2 = -17 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 = -17 + 169 Reorder the terms: 169 + 26x + x2 = -17 + 169 Combine like terms: -17 + 169 = 152 169 + 26x + x2 = 152 Factor a perfect square on the left side: (x + 13)(x + 13) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (x + 13) equal to 12.328828006 and -12.328828006.Subproblem 1
x + 13 = 12.328828006 Simplifying x + 13 = 12.328828006 Reorder the terms: 13 + x = 12.328828006 Solving 13 + x = 12.328828006 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 = 12.328828006 + -13 Combine like terms: 13 + -13 = 0 0 + x = 12.328828006 + -13 x = 12.328828006 + -13 Combine like terms: 12.328828006 + -13 = -0.671171994 x = -0.671171994 Simplifying x = -0.671171994Subproblem 2
x + 13 = -12.328828006 Simplifying x + 13 = -12.328828006 Reorder the terms: 13 + x = -12.328828006 Solving 13 + x = -12.328828006 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 = -12.328828006 + -13 Combine like terms: 13 + -13 = 0 0 + x = -12.328828006 + -13 x = -12.328828006 + -13 Combine like terms: -12.328828006 + -13 = -25.328828006 x = -25.328828006 Simplifying x = -25.328828006Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.671171994, -25.328828006}
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