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Simplifying (x + 5)(2x + 1) + -1(x + -3)(x + -5) = (-1(10x + 14)) Reorder the terms: (5 + x)(2x + 1) + -1(x + -3)(x + -5) = (-1(10x + 14)) Reorder the terms: (5 + x)(1 + 2x) + -1(x + -3)(x + -5) = (-1(10x + 14)) Multiply (5 + x) * (1 + 2x) (5(1 + 2x) + x(1 + 2x)) + -1(x + -3)(x + -5) = (-1(10x + 14)) ((1 * 5 + 2x * 5) + x(1 + 2x)) + -1(x + -3)(x + -5) = (-1(10x + 14)) ((5 + 10x) + x(1 + 2x)) + -1(x + -3)(x + -5) = (-1(10x + 14)) (5 + 10x + (1 * x + 2x * x)) + -1(x + -3)(x + -5) = (-1(10x + 14)) (5 + 10x + (1x + 2x2)) + -1(x + -3)(x + -5) = (-1(10x + 14)) Combine like terms: 10x + 1x = 11x (5 + 11x + 2x2) + -1(x + -3)(x + -5) = (-1(10x + 14)) Reorder the terms: 5 + 11x + 2x2 + -1(-3 + x)(x + -5) = (-1(10x + 14)) Reorder the terms: 5 + 11x + 2x2 + -1(-3 + x)(-5 + x) = (-1(10x + 14)) Multiply (-3 + x) * (-5 + x) 5 + 11x + 2x2 + -1(-3(-5 + x) + x(-5 + x)) = (-1(10x + 14)) 5 + 11x + 2x2 + -1((-5 * -3 + x * -3) + x(-5 + x)) = (-1(10x + 14)) 5 + 11x + 2x2 + -1((15 + -3x) + x(-5 + x)) = (-1(10x + 14)) 5 + 11x + 2x2 + -1(15 + -3x + (-5 * x + x * x)) = (-1(10x + 14)) 5 + 11x + 2x2 + -1(15 + -3x + (-5x + x2)) = (-1(10x + 14)) Combine like terms: -3x + -5x = -8x 5 + 11x + 2x2 + -1(15 + -8x + x2) = (-1(10x + 14)) 5 + 11x + 2x2 + (15 * -1 + -8x * -1 + x2 * -1) = (-1(10x + 14)) 5 + 11x + 2x2 + (-15 + 8x + -1x2) = (-1(10x + 14)) Reorder the terms: 5 + -15 + 11x + 8x + 2x2 + -1x2 = (-1(10x + 14)) Combine like terms: 5 + -15 = -10 -10 + 11x + 8x + 2x2 + -1x2 = (-1(10x + 14)) Combine like terms: 11x + 8x = 19x -10 + 19x + 2x2 + -1x2 = (-1(10x + 14)) Combine like terms: 2x2 + -1x2 = 1x2 -10 + 19x + 1x2 = (-1(10x + 14)) Reorder the terms: -10 + 19x + 1x2 = (-1(14 + 10x)) -10 + 19x + 1x2 = ((14 * -1 + 10x * -1)) -10 + 19x + 1x2 = ((-14 + -10x)) -10 + 19x + 1x2 = (-14 + -10x) Remove parenthesis around (-14 + -10x) -10 + 19x + 1x2 = -14 + -10x Solving -10 + 19x + 1x2 = -14 + -10x Solving for variable 'x'. Reorder the terms: -10 + 14 + 19x + 10x + 1x2 = -14 + -10x + 14 + 10x Combine like terms: -10 + 14 = 4 4 + 19x + 10x + 1x2 = -14 + -10x + 14 + 10x Combine like terms: 19x + 10x = 29x 4 + 29x + 1x2 = -14 + -10x + 14 + 10x Reorder the terms: 4 + 29x + 1x2 = -14 + 14 + -10x + 10x Combine like terms: -14 + 14 = 0 4 + 29x + 1x2 = 0 + -10x + 10x 4 + 29x + 1x2 = -10x + 10x Combine like terms: -10x + 10x = 0 4 + 29x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 29x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 29x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 29x + x2 = 0 + -4 29x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 29x + x2 = -4 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = -4 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -4 + 210.25 Combine like terms: -4 + 210.25 = 206.25 210.25 + 29x + x2 = 206.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 206.25 Calculate the square root of the right side: 14.361406616 Break this problem into two subproblems by setting (x + 14.5) equal to 14.361406616 and -14.361406616.Subproblem 1
x + 14.5 = 14.361406616 Simplifying x + 14.5 = 14.361406616 Reorder the terms: 14.5 + x = 14.361406616 Solving 14.5 + x = 14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 14.361406616 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 14.361406616 + -14.5 x = 14.361406616 + -14.5 Combine like terms: 14.361406616 + -14.5 = -0.138593384 x = -0.138593384 Simplifying x = -0.138593384Subproblem 2
x + 14.5 = -14.361406616 Simplifying x + 14.5 = -14.361406616 Reorder the terms: 14.5 + x = -14.361406616 Solving 14.5 + x = -14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -14.361406616 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -14.361406616 + -14.5 x = -14.361406616 + -14.5 Combine like terms: -14.361406616 + -14.5 = -28.861406616 x = -28.861406616 Simplifying x = -28.861406616Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.138593384, -28.861406616}
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