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Simplifying 26x + -1x2 = -128 Solving 26x + -1x2 = -128 Solving for variable 'x'. Reorder the terms: 128 + 26x + -1x2 = -128 + 128 Combine like terms: -128 + 128 = 0 128 + 26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -128 + -26x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + -26x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + -26x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -26x + x2 = 0 + 128 -26x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 -26x + x2 = 128 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 = 128 + 169 Reorder the terms: 169 + -26x + x2 = 128 + 169 Combine like terms: 128 + 169 = 297 169 + -26x + x2 = 297 Factor a perfect square on the left side: (x + -13)(x + -13) = 297 Calculate the square root of the right side: 17.23368794 Break this problem into two subproblems by setting (x + -13) equal to 17.23368794 and -17.23368794.Subproblem 1
x + -13 = 17.23368794 Simplifying x + -13 = 17.23368794 Reorder the terms: -13 + x = 17.23368794 Solving -13 + x = 17.23368794 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 = 17.23368794 + 13 Combine like terms: -13 + 13 = 0 0 + x = 17.23368794 + 13 x = 17.23368794 + 13 Combine like terms: 17.23368794 + 13 = 30.23368794 x = 30.23368794 Simplifying x = 30.23368794Subproblem 2
x + -13 = -17.23368794 Simplifying x + -13 = -17.23368794 Reorder the terms: -13 + x = -17.23368794 Solving -13 + x = -17.23368794 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 = -17.23368794 + 13 Combine like terms: -13 + 13 = 0 0 + x = -17.23368794 + 13 x = -17.23368794 + 13 Combine like terms: -17.23368794 + 13 = -4.23368794 x = -4.23368794 Simplifying x = -4.23368794Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.23368794, -4.23368794}
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