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Simplifying 0 = -1x2 + 26x + -46 Reorder the terms: 0 = -46 + 26x + -1x2 Solving 0 = -46 + 26x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 46 = 46 46 + -26x + x2 = -46 + 26x + -1x2 + 46 + -26x + x2 Reorder the terms: 46 + -26x + x2 = -46 + 46 + 26x + -26x + -1x2 + x2 Combine like terms: -46 + 46 = 0 46 + -26x + x2 = 0 + 26x + -26x + -1x2 + x2 46 + -26x + x2 = 26x + -26x + -1x2 + x2 Combine like terms: 26x + -26x = 0 46 + -26x + x2 = 0 + -1x2 + x2 46 + -26x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 46 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + -26x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + -26x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -26x + x2 = 0 + -46 -26x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 -26x + x2 = -46 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 = -46 + 169 Reorder the terms: 169 + -26x + x2 = -46 + 169 Combine like terms: -46 + 169 = 123 169 + -26x + x2 = 123 Factor a perfect square on the left side: (x + -13)(x + -13) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (x + -13) equal to 11.090536506 and -11.090536506.Subproblem 1
x + -13 = 11.090536506 Simplifying x + -13 = 11.090536506 Reorder the terms: -13 + x = 11.090536506 Solving -13 + x = 11.090536506 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 = 11.090536506 + 13 Combine like terms: -13 + 13 = 0 0 + x = 11.090536506 + 13 x = 11.090536506 + 13 Combine like terms: 11.090536506 + 13 = 24.090536506 x = 24.090536506 Simplifying x = 24.090536506Subproblem 2
x + -13 = -11.090536506 Simplifying x + -13 = -11.090536506 Reorder the terms: -13 + x = -11.090536506 Solving -13 + x = -11.090536506 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 = -11.090536506 + 13 Combine like terms: -13 + 13 = 0 0 + x = -11.090536506 + 13 x = -11.090536506 + 13 Combine like terms: -11.090536506 + 13 = 1.909463494 x = 1.909463494 Simplifying x = 1.909463494Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.090536506, 1.909463494}
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