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Simplifying 2x + 26 + 81 = x2 Reorder the terms: 26 + 81 + 2x = x2 Combine like terms: 26 + 81 = 107 107 + 2x = x2 Solving 107 + 2x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 107 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -107 + -2x + x2 = 0 Move the constant term to the right: Add '107' to each side of the equation. -107 + -2x + 107 + x2 = 0 + 107 Reorder the terms: -107 + 107 + -2x + x2 = 0 + 107 Combine like terms: -107 + 107 = 0 0 + -2x + x2 = 0 + 107 -2x + x2 = 0 + 107 Combine like terms: 0 + 107 = 107 -2x + x2 = 107 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 107 + 1 Reorder the terms: 1 + -2x + x2 = 107 + 1 Combine like terms: 107 + 1 = 108 1 + -2x + x2 = 108 Factor a perfect square on the left side: (x + -1)(x + -1) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -1) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -1 = 10.392304845 Simplifying x + -1 = 10.392304845 Reorder the terms: -1 + x = 10.392304845 Solving -1 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.392304845 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.392304845 + 1 x = 10.392304845 + 1 Combine like terms: 10.392304845 + 1 = 11.392304845 x = 11.392304845 Simplifying x = 11.392304845Subproblem 2
x + -1 = -10.392304845 Simplifying x + -1 = -10.392304845 Reorder the terms: -1 + x = -10.392304845 Solving -1 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.392304845 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.392304845 + 1 x = -10.392304845 + 1 Combine like terms: -10.392304845 + 1 = -9.392304845 x = -9.392304845 Simplifying x = -9.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.392304845, -9.392304845}
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