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Simplifying (3x + -7)(3x + -7) = (2x + 1)(2x + 1) Reorder the terms: (-7 + 3x)(3x + -7) = (2x + 1)(2x + 1) Reorder the terms: (-7 + 3x)(-7 + 3x) = (2x + 1)(2x + 1) Multiply (-7 + 3x) * (-7 + 3x) (-7(-7 + 3x) + 3x * (-7 + 3x)) = (2x + 1)(2x + 1) ((-7 * -7 + 3x * -7) + 3x * (-7 + 3x)) = (2x + 1)(2x + 1) ((49 + -21x) + 3x * (-7 + 3x)) = (2x + 1)(2x + 1) (49 + -21x + (-7 * 3x + 3x * 3x)) = (2x + 1)(2x + 1) (49 + -21x + (-21x + 9x2)) = (2x + 1)(2x + 1) Combine like terms: -21x + -21x = -42x (49 + -42x + 9x2) = (2x + 1)(2x + 1) Reorder the terms: 49 + -42x + 9x2 = (1 + 2x)(2x + 1) Reorder the terms: 49 + -42x + 9x2 = (1 + 2x)(1 + 2x) Multiply (1 + 2x) * (1 + 2x) 49 + -42x + 9x2 = (1(1 + 2x) + 2x * (1 + 2x)) 49 + -42x + 9x2 = ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) 49 + -42x + 9x2 = ((1 + 2x) + 2x * (1 + 2x)) 49 + -42x + 9x2 = (1 + 2x + (1 * 2x + 2x * 2x)) 49 + -42x + 9x2 = (1 + 2x + (2x + 4x2)) Combine like terms: 2x + 2x = 4x 49 + -42x + 9x2 = (1 + 4x + 4x2) Solving 49 + -42x + 9x2 = 1 + 4x + 4x2 Solving for variable 'x'. Reorder the terms: 49 + -1 + -42x + -4x + 9x2 + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2 Combine like terms: 49 + -1 = 48 48 + -42x + -4x + 9x2 + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2 Combine like terms: -42x + -4x = -46x 48 + -46x + 9x2 + -4x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 48 + -46x + 5x2 = 1 + 4x + 4x2 + -1 + -4x + -4x2 Reorder the terms: 48 + -46x + 5x2 = 1 + -1 + 4x + -4x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 48 + -46x + 5x2 = 0 + 4x + -4x + 4x2 + -4x2 48 + -46x + 5x2 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 48 + -46x + 5x2 = 0 + 4x2 + -4x2 48 + -46x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 48 + -46x + 5x2 = 0 Factor a trinomial. (6 + -5x)(8 + -1x) = 0Subproblem 1
Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {1.2, 8}
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