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Simplifying x2 + 26x + 156 = 0 Reorder the terms: 156 + 26x + x2 = 0 Solving 156 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-156' to each side of the equation. 156 + 26x + -156 + x2 = 0 + -156 Reorder the terms: 156 + -156 + 26x + x2 = 0 + -156 Combine like terms: 156 + -156 = 0 0 + 26x + x2 = 0 + -156 26x + x2 = 0 + -156 Combine like terms: 0 + -156 = -156 26x + x2 = -156 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 = -156 + 169 Reorder the terms: 169 + 26x + x2 = -156 + 169 Combine like terms: -156 + 169 = 13 169 + 26x + x2 = 13 Factor a perfect square on the left side: (x + 13)(x + 13) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 13) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 13 = 3.605551275 Simplifying x + 13 = 3.605551275 Reorder the terms: 13 + x = 3.605551275 Solving 13 + x = 3.605551275 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 = 3.605551275 + -13 Combine like terms: 13 + -13 = 0 0 + x = 3.605551275 + -13 x = 3.605551275 + -13 Combine like terms: 3.605551275 + -13 = -9.394448725 x = -9.394448725 Simplifying x = -9.394448725Subproblem 2
x + 13 = -3.605551275 Simplifying x + 13 = -3.605551275 Reorder the terms: 13 + x = -3.605551275 Solving 13 + x = -3.605551275 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 = -3.605551275 + -13 Combine like terms: 13 + -13 = 0 0 + x = -3.605551275 + -13 x = -3.605551275 + -13 Combine like terms: -3.605551275 + -13 = -16.605551275 x = -16.605551275 Simplifying x = -16.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.394448725, -16.605551275}
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