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Simplifying x2 + -26x + -24 = 0 Reorder the terms: -24 + -26x + x2 = 0 Solving -24 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -26x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -26x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -26x + x2 = 0 + 24 -26x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -26x + x2 = 24 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 = 24 + 169 Reorder the terms: 169 + -26x + x2 = 24 + 169 Combine like terms: 24 + 169 = 193 169 + -26x + x2 = 193 Factor a perfect square on the left side: (x + -13)(x + -13) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + -13) equal to 13.892443989 and -13.892443989.Subproblem 1
x + -13 = 13.892443989 Simplifying x + -13 = 13.892443989 Reorder the terms: -13 + x = 13.892443989 Solving -13 + x = 13.892443989 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 = 13.892443989 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.892443989 + 13 x = 13.892443989 + 13 Combine like terms: 13.892443989 + 13 = 26.892443989 x = 26.892443989 Simplifying x = 26.892443989Subproblem 2
x + -13 = -13.892443989 Simplifying x + -13 = -13.892443989 Reorder the terms: -13 + x = -13.892443989 Solving -13 + x = -13.892443989 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 = -13.892443989 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.892443989 + 13 x = -13.892443989 + 13 Combine like terms: -13.892443989 + 13 = -0.892443989 x = -0.892443989 Simplifying x = -0.892443989Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.892443989, -0.892443989}
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