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Simplifying 135 + -1(6x + 9) = 6(x + 8) * x Reorder the terms: 135 + -1(9 + 6x) = 6(x + 8) * x 135 + (9 * -1 + 6x * -1) = 6(x + 8) * x 135 + (-9 + -6x) = 6(x + 8) * x Combine like terms: 135 + -9 = 126 126 + -6x = 6(x + 8) * x Reorder the terms: 126 + -6x = 6(8 + x) * x Reorder the terms for easier multiplication: 126 + -6x = 6x(8 + x) 126 + -6x = (8 * 6x + x * 6x) 126 + -6x = (48x + 6x2) Solving 126 + -6x = 48x + 6x2 Solving for variable 'x'. Combine like terms: -6x + -48x = -54x 126 + -54x + -6x2 = 48x + 6x2 + -48x + -6x2 Reorder the terms: 126 + -54x + -6x2 = 48x + -48x + 6x2 + -6x2 Combine like terms: 48x + -48x = 0 126 + -54x + -6x2 = 0 + 6x2 + -6x2 126 + -54x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 126 + -54x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(21 + -9x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(21 + -9x + -1x2)' equal to zero and attempt to solve: Simplifying 21 + -9x + -1x2 = 0 Solving 21 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 9x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 9x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 9x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 9x + x2 = 0 + 21 9x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 9x + x2 = 21 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 21 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 21 + 20.25 Combine like terms: 21 + 20.25 = 41.25 20.25 + 9x + x2 = 41.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + 4.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + 4.5 = 6.422616289 Simplifying x + 4.5 = 6.422616289 Reorder the terms: 4.5 + x = 6.422616289 Solving 4.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 6.422616289 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.422616289 + -4.5 x = 6.422616289 + -4.5 Combine like terms: 6.422616289 + -4.5 = 1.922616289 x = 1.922616289 Simplifying x = 1.922616289Subproblem 2
x + 4.5 = -6.422616289 Simplifying x + 4.5 = -6.422616289 Reorder the terms: 4.5 + x = -6.422616289 Solving 4.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -6.422616289 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.422616289 + -4.5 x = -6.422616289 + -4.5 Combine like terms: -6.422616289 + -4.5 = -10.922616289 x = -10.922616289 Simplifying x = -10.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.922616289, -10.922616289}Solution
x = {1.922616289, -10.922616289}
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