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Simplifying (3x + -7)(3x + -7) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) Reorder the terms: (-7 + 3x)(3x + -7) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) Reorder the terms: (-7 + 3x)(-7 + 3x) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) Multiply (-7 + 3x) * (-7 + 3x) (-7(-7 + 3x) + 3x * (-7 + 3x)) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) ((-7 * -7 + 3x * -7) + 3x * (-7 + 3x)) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) ((49 + -21x) + 3x * (-7 + 3x)) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) (49 + -21x + (-7 * 3x + 3x * 3x)) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) (49 + -21x + (-21x + 9x2)) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) Combine like terms: -21x + -21x = -42x (49 + -42x + 9x2) + -5(2x + 1)(x + -2) = -1x + -1(-1(3x + 1)) Reorder the terms: 49 + -42x + 9x2 + -5(1 + 2x)(x + -2) = -1x + -1(-1(3x + 1)) Reorder the terms: 49 + -42x + 9x2 + -5(1 + 2x)(-2 + x) = -1x + -1(-1(3x + 1)) Multiply (1 + 2x) * (-2 + x) 49 + -42x + 9x2 + -5(1(-2 + x) + 2x * (-2 + x)) = -1x + -1(-1(3x + 1)) 49 + -42x + 9x2 + -5((-2 * 1 + x * 1) + 2x * (-2 + x)) = -1x + -1(-1(3x + 1)) 49 + -42x + 9x2 + -5((-2 + 1x) + 2x * (-2 + x)) = -1x + -1(-1(3x + 1)) 49 + -42x + 9x2 + -5(-2 + 1x + (-2 * 2x + x * 2x)) = -1x + -1(-1(3x + 1)) 49 + -42x + 9x2 + -5(-2 + 1x + (-4x + 2x2)) = -1x + -1(-1(3x + 1)) Combine like terms: 1x + -4x = -3x 49 + -42x + 9x2 + -5(-2 + -3x + 2x2) = -1x + -1(-1(3x + 1)) 49 + -42x + 9x2 + (-2 * -5 + -3x * -5 + 2x2 * -5) = -1x + -1(-1(3x + 1)) 49 + -42x + 9x2 + (10 + 15x + -10x2) = -1x + -1(-1(3x + 1)) Reorder the terms: 49 + 10 + -42x + 15x + 9x2 + -10x2 = -1x + -1(-1(3x + 1)) Combine like terms: 49 + 10 = 59 59 + -42x + 15x + 9x2 + -10x2 = -1x + -1(-1(3x + 1)) Combine like terms: -42x + 15x = -27x 59 + -27x + 9x2 + -10x2 = -1x + -1(-1(3x + 1)) Combine like terms: 9x2 + -10x2 = -1x2 59 + -27x + -1x2 = -1x + -1(-1(3x + 1)) Reorder the terms: 59 + -27x + -1x2 = -1x + -1(-1(1 + 3x)) 59 + -27x + -1x2 = -1x + -1((1 * -1 + 3x * -1)) 59 + -27x + -1x2 = -1x + -1((-1 + -3x)) 59 + -27x + -1x2 = -1x + (-1 * -1 + -3x * -1) 59 + -27x + -1x2 = -1x + (1 + 3x) Reorder the terms: 59 + -27x + -1x2 = 1 + -1x + 3x Combine like terms: -1x + 3x = 2x 59 + -27x + -1x2 = 1 + 2x Solving 59 + -27x + -1x2 = 1 + 2x Solving for variable 'x'. Reorder the terms: 59 + -1 + -27x + -2x + -1x2 = 1 + 2x + -1 + -2x Combine like terms: 59 + -1 = 58 58 + -27x + -2x + -1x2 = 1 + 2x + -1 + -2x Combine like terms: -27x + -2x = -29x 58 + -29x + -1x2 = 1 + 2x + -1 + -2x Reorder the terms: 58 + -29x + -1x2 = 1 + -1 + 2x + -2x Combine like terms: 1 + -1 = 0 58 + -29x + -1x2 = 0 + 2x + -2x 58 + -29x + -1x2 = 2x + -2x Combine like terms: 2x + -2x = 0 58 + -29x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -58 + 29x + x2 = 0 Move the constant term to the right: Add '58' to each side of the equation. -58 + 29x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 29x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 29x + x2 = 0 + 58 29x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 29x + x2 = 58 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 = 58 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 58 + 210.25 Combine like terms: 58 + 210.25 = 268.25 210.25 + 29x + x2 = 268.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 268.25 Calculate the square root of the right side: 16.378339354 Break this problem into two subproblems by setting (x + 14.5) equal to 16.378339354 and -16.378339354.Subproblem 1
x + 14.5 = 16.378339354 Simplifying x + 14.5 = 16.378339354 Reorder the terms: 14.5 + x = 16.378339354 Solving 14.5 + x = 16.378339354 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 = 16.378339354 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 16.378339354 + -14.5 x = 16.378339354 + -14.5 Combine like terms: 16.378339354 + -14.5 = 1.878339354 x = 1.878339354 Simplifying x = 1.878339354Subproblem 2
x + 14.5 = -16.378339354 Simplifying x + 14.5 = -16.378339354 Reorder the terms: 14.5 + x = -16.378339354 Solving 14.5 + x = -16.378339354 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 = -16.378339354 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -16.378339354 + -14.5 x = -16.378339354 + -14.5 Combine like terms: -16.378339354 + -14.5 = -30.878339354 x = -30.878339354 Simplifying x = -30.878339354Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.878339354, -30.878339354}
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