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Simplifying x2 + -26x + 50 = 0 Reorder the terms: 50 + -26x + x2 = 0 Solving 50 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -26x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -26x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -26x + x2 = 0 + -50 -26x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -26x + x2 = -50 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 = -50 + 169 Reorder the terms: 169 + -26x + x2 = -50 + 169 Combine like terms: -50 + 169 = 119 169 + -26x + x2 = 119 Factor a perfect square on the left side: (x + -13)(x + -13) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + -13) equal to 10.908712115 and -10.908712115.Subproblem 1
x + -13 = 10.908712115 Simplifying x + -13 = 10.908712115 Reorder the terms: -13 + x = 10.908712115 Solving -13 + x = 10.908712115 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 = 10.908712115 + 13 Combine like terms: -13 + 13 = 0 0 + x = 10.908712115 + 13 x = 10.908712115 + 13 Combine like terms: 10.908712115 + 13 = 23.908712115 x = 23.908712115 Simplifying x = 23.908712115Subproblem 2
x + -13 = -10.908712115 Simplifying x + -13 = -10.908712115 Reorder the terms: -13 + x = -10.908712115 Solving -13 + x = -10.908712115 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 = -10.908712115 + 13 Combine like terms: -13 + 13 = 0 0 + x = -10.908712115 + 13 x = -10.908712115 + 13 Combine like terms: -10.908712115 + 13 = 2.091287885 x = 2.091287885 Simplifying x = 2.091287885Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.908712115, 2.091287885}
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