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Simplifying x2 + 26x = 68 Reorder the terms: 26x + x2 = 68 Solving 26x + x2 = 68 Solving for variable 'x'. Reorder the terms: -68 + 26x + x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 26x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 26x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 26x + x2 = 0 + 68 26x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 26x + x2 = 68 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 = 68 + 169 Reorder the terms: 169 + 26x + x2 = 68 + 169 Combine like terms: 68 + 169 = 237 169 + 26x + x2 = 237 Factor a perfect square on the left side: (x + 13)(x + 13) = 237 Calculate the square root of the right side: 15.394804318 Break this problem into two subproblems by setting (x + 13) equal to 15.394804318 and -15.394804318.Subproblem 1
x + 13 = 15.394804318 Simplifying x + 13 = 15.394804318 Reorder the terms: 13 + x = 15.394804318 Solving 13 + x = 15.394804318 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 = 15.394804318 + -13 Combine like terms: 13 + -13 = 0 0 + x = 15.394804318 + -13 x = 15.394804318 + -13 Combine like terms: 15.394804318 + -13 = 2.394804318 x = 2.394804318 Simplifying x = 2.394804318Subproblem 2
x + 13 = -15.394804318 Simplifying x + 13 = -15.394804318 Reorder the terms: 13 + x = -15.394804318 Solving 13 + x = -15.394804318 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 = -15.394804318 + -13 Combine like terms: 13 + -13 = 0 0 + x = -15.394804318 + -13 x = -15.394804318 + -13 Combine like terms: -15.394804318 + -13 = -28.394804318 x = -28.394804318 Simplifying x = -28.394804318Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.394804318, -28.394804318}
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