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Simplifying x2 + -26x + -105 = 0 Reorder the terms: -105 + -26x + x2 = 0 Solving -105 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + -26x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + -26x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + -26x + x2 = 0 + 105 -26x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 -26x + x2 = 105 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 = 105 + 169 Reorder the terms: 169 + -26x + x2 = 105 + 169 Combine like terms: 105 + 169 = 274 169 + -26x + x2 = 274 Factor a perfect square on the left side: (x + -13)(x + -13) = 274 Calculate the square root of the right side: 16.552945357 Break this problem into two subproblems by setting (x + -13) equal to 16.552945357 and -16.552945357.Subproblem 1
x + -13 = 16.552945357 Simplifying x + -13 = 16.552945357 Reorder the terms: -13 + x = 16.552945357 Solving -13 + x = 16.552945357 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 = 16.552945357 + 13 Combine like terms: -13 + 13 = 0 0 + x = 16.552945357 + 13 x = 16.552945357 + 13 Combine like terms: 16.552945357 + 13 = 29.552945357 x = 29.552945357 Simplifying x = 29.552945357Subproblem 2
x + -13 = -16.552945357 Simplifying x + -13 = -16.552945357 Reorder the terms: -13 + x = -16.552945357 Solving -13 + x = -16.552945357 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 = -16.552945357 + 13 Combine like terms: -13 + 13 = 0 0 + x = -16.552945357 + 13 x = -16.552945357 + 13 Combine like terms: -16.552945357 + 13 = -3.552945357 x = -3.552945357 Simplifying x = -3.552945357Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.552945357, -3.552945357}
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