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Simplifying x2 + -26x + -62 = 0 Reorder the terms: -62 + -26x + x2 = 0 Solving -62 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + -26x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -26x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -26x + x2 = 0 + 62 -26x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -26x + x2 = 62 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 = 62 + 169 Reorder the terms: 169 + -26x + x2 = 62 + 169 Combine like terms: 62 + 169 = 231 169 + -26x + x2 = 231 Factor a perfect square on the left side: (x + -13)(x + -13) = 231 Calculate the square root of the right side: 15.198684154 Break this problem into two subproblems by setting (x + -13) equal to 15.198684154 and -15.198684154.Subproblem 1
x + -13 = 15.198684154 Simplifying x + -13 = 15.198684154 Reorder the terms: -13 + x = 15.198684154 Solving -13 + x = 15.198684154 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 = 15.198684154 + 13 Combine like terms: -13 + 13 = 0 0 + x = 15.198684154 + 13 x = 15.198684154 + 13 Combine like terms: 15.198684154 + 13 = 28.198684154 x = 28.198684154 Simplifying x = 28.198684154Subproblem 2
x + -13 = -15.198684154 Simplifying x + -13 = -15.198684154 Reorder the terms: -13 + x = -15.198684154 Solving -13 + x = -15.198684154 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 = -15.198684154 + 13 Combine like terms: -13 + 13 = 0 0 + x = -15.198684154 + 13 x = -15.198684154 + 13 Combine like terms: -15.198684154 + 13 = -2.198684154 x = -2.198684154 Simplifying x = -2.198684154Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.198684154, -2.198684154}
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