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Simplifying x2 + -26x + -45 = 0 Reorder the terms: -45 + -26x + x2 = 0 Solving -45 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -26x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -26x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -26x + x2 = 0 + 45 -26x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -26x + x2 = 45 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 = 45 + 169 Reorder the terms: 169 + -26x + x2 = 45 + 169 Combine like terms: 45 + 169 = 214 169 + -26x + x2 = 214 Factor a perfect square on the left side: (x + -13)(x + -13) = 214 Calculate the square root of the right side: 14.628738838 Break this problem into two subproblems by setting (x + -13) equal to 14.628738838 and -14.628738838.Subproblem 1
x + -13 = 14.628738838 Simplifying x + -13 = 14.628738838 Reorder the terms: -13 + x = 14.628738838 Solving -13 + x = 14.628738838 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 = 14.628738838 + 13 Combine like terms: -13 + 13 = 0 0 + x = 14.628738838 + 13 x = 14.628738838 + 13 Combine like terms: 14.628738838 + 13 = 27.628738838 x = 27.628738838 Simplifying x = 27.628738838Subproblem 2
x + -13 = -14.628738838 Simplifying x + -13 = -14.628738838 Reorder the terms: -13 + x = -14.628738838 Solving -13 + x = -14.628738838 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 = -14.628738838 + 13 Combine like terms: -13 + 13 = 0 0 + x = -14.628738838 + 13 x = -14.628738838 + 13 Combine like terms: -14.628738838 + 13 = -1.628738838 x = -1.628738838 Simplifying x = -1.628738838Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.628738838, -1.628738838}
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