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Simplifying x2 + -26x + 58 = 0 Reorder the terms: 58 + -26x + x2 = 0 Solving 58 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + -26x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + -26x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + -26x + x2 = 0 + -58 -26x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 -26x + x2 = -58 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 = -58 + 169 Reorder the terms: 169 + -26x + x2 = -58 + 169 Combine like terms: -58 + 169 = 111 169 + -26x + x2 = 111 Factor a perfect square on the left side: (x + -13)(x + -13) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (x + -13) equal to 10.535653753 and -10.535653753.Subproblem 1
x + -13 = 10.535653753 Simplifying x + -13 = 10.535653753 Reorder the terms: -13 + x = 10.535653753 Solving -13 + x = 10.535653753 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 = 10.535653753 + 13 Combine like terms: -13 + 13 = 0 0 + x = 10.535653753 + 13 x = 10.535653753 + 13 Combine like terms: 10.535653753 + 13 = 23.535653753 x = 23.535653753 Simplifying x = 23.535653753Subproblem 2
x + -13 = -10.535653753 Simplifying x + -13 = -10.535653753 Reorder the terms: -13 + x = -10.535653753 Solving -13 + x = -10.535653753 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 = -10.535653753 + 13 Combine like terms: -13 + 13 = 0 0 + x = -10.535653753 + 13 x = -10.535653753 + 13 Combine like terms: -10.535653753 + 13 = 2.464346247 x = 2.464346247 Simplifying x = 2.464346247Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.535653753, 2.464346247}
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