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Simplifying x2 + -10x + -25 + 2x2 + x + -2x + -1 = 13x + 26 Reorder the terms: -25 + -1 + -10x + x + -2x + x2 + 2x2 = 13x + 26 Combine like terms: -25 + -1 = -26 -26 + -10x + x + -2x + x2 + 2x2 = 13x + 26 Combine like terms: -10x + x = -9x -26 + -9x + -2x + x2 + 2x2 = 13x + 26 Combine like terms: -9x + -2x = -11x -26 + -11x + x2 + 2x2 = 13x + 26 Combine like terms: x2 + 2x2 = 3x2 -26 + -11x + 3x2 = 13x + 26 Reorder the terms: -26 + -11x + 3x2 = 26 + 13x Solving -26 + -11x + 3x2 = 26 + 13x Solving for variable 'x'. Reorder the terms: -26 + -26 + -11x + -13x + 3x2 = 26 + 13x + -26 + -13x Combine like terms: -26 + -26 = -52 -52 + -11x + -13x + 3x2 = 26 + 13x + -26 + -13x Combine like terms: -11x + -13x = -24x -52 + -24x + 3x2 = 26 + 13x + -26 + -13x Reorder the terms: -52 + -24x + 3x2 = 26 + -26 + 13x + -13x Combine like terms: 26 + -26 = 0 -52 + -24x + 3x2 = 0 + 13x + -13x -52 + -24x + 3x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -52 + -24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -17.33333333 + -8x + x2 = 0 Move the constant term to the right: Add '17.33333333' to each side of the equation. -17.33333333 + -8x + 17.33333333 + x2 = 0 + 17.33333333 Reorder the terms: -17.33333333 + 17.33333333 + -8x + x2 = 0 + 17.33333333 Combine like terms: -17.33333333 + 17.33333333 = 0.00000000 0.00000000 + -8x + x2 = 0 + 17.33333333 -8x + x2 = 0 + 17.33333333 Combine like terms: 0 + 17.33333333 = 17.33333333 -8x + x2 = 17.33333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 17.33333333 + 16 Reorder the terms: 16 + -8x + x2 = 17.33333333 + 16 Combine like terms: 17.33333333 + 16 = 33.33333333 16 + -8x + x2 = 33.33333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 33.33333333 Calculate the square root of the right side: 5.773502692 Break this problem into two subproblems by setting (x + -4) equal to 5.773502692 and -5.773502692.Subproblem 1
x + -4 = 5.773502692 Simplifying x + -4 = 5.773502692 Reorder the terms: -4 + x = 5.773502692 Solving -4 + x = 5.773502692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.773502692 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.773502692 + 4 x = 5.773502692 + 4 Combine like terms: 5.773502692 + 4 = 9.773502692 x = 9.773502692 Simplifying x = 9.773502692Subproblem 2
x + -4 = -5.773502692 Simplifying x + -4 = -5.773502692 Reorder the terms: -4 + x = -5.773502692 Solving -4 + x = -5.773502692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.773502692 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.773502692 + 4 x = -5.773502692 + 4 Combine like terms: -5.773502692 + 4 = -1.773502692 x = -1.773502692 Simplifying x = -1.773502692Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.773502692, -1.773502692}
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