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Simplifying x2 + 26x + 7 = 0 Reorder the terms: 7 + 26x + x2 = 0 Solving 7 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 26x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 26x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 26x + x2 = 0 + -7 26x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 26x + x2 = -7 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 = -7 + 169 Reorder the terms: 169 + 26x + x2 = -7 + 169 Combine like terms: -7 + 169 = 162 169 + 26x + x2 = 162 Factor a perfect square on the left side: (x + 13)(x + 13) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (x + 13) equal to 12.727922061 and -12.727922061.Subproblem 1
x + 13 = 12.727922061 Simplifying x + 13 = 12.727922061 Reorder the terms: 13 + x = 12.727922061 Solving 13 + x = 12.727922061 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 = 12.727922061 + -13 Combine like terms: 13 + -13 = 0 0 + x = 12.727922061 + -13 x = 12.727922061 + -13 Combine like terms: 12.727922061 + -13 = -0.272077939 x = -0.272077939 Simplifying x = -0.272077939Subproblem 2
x + 13 = -12.727922061 Simplifying x + 13 = -12.727922061 Reorder the terms: 13 + x = -12.727922061 Solving 13 + x = -12.727922061 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 = -12.727922061 + -13 Combine like terms: 13 + -13 = 0 0 + x = -12.727922061 + -13 x = -12.727922061 + -13 Combine like terms: -12.727922061 + -13 = -25.727922061 x = -25.727922061 Simplifying x = -25.727922061Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.272077939, -25.727922061}
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