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Simplifying 5(x + -8) * x = 6(x + -3) + -22 Reorder the terms: 5(-8 + x) * x = 6(x + -3) + -22 Reorder the terms for easier multiplication: 5x(-8 + x) = 6(x + -3) + -22 (-8 * 5x + x * 5x) = 6(x + -3) + -22 (-40x + 5x2) = 6(x + -3) + -22 Reorder the terms: -40x + 5x2 = 6(-3 + x) + -22 -40x + 5x2 = (-3 * 6 + x * 6) + -22 -40x + 5x2 = (-18 + 6x) + -22 Reorder the terms: -40x + 5x2 = -18 + -22 + 6x Combine like terms: -18 + -22 = -40 -40x + 5x2 = -40 + 6x Solving -40x + 5x2 = -40 + 6x Solving for variable 'x'. Reorder the terms: 40 + -40x + -6x + 5x2 = -40 + 6x + 40 + -6x Combine like terms: -40x + -6x = -46x 40 + -46x + 5x2 = -40 + 6x + 40 + -6x Reorder the terms: 40 + -46x + 5x2 = -40 + 40 + 6x + -6x Combine like terms: -40 + 40 = 0 40 + -46x + 5x2 = 0 + 6x + -6x 40 + -46x + 5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 40 + -46x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8 + -9.2x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -9.2x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -9.2x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9.2x + x2 = 0 + -8 -9.2x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -9.2x + x2 = -8 The x term is -9.2x. Take half its coefficient (-4.6). Square it (21.16) and add it to both sides. Add '21.16' to each side of the equation. -9.2x + 21.16 + x2 = -8 + 21.16 Reorder the terms: 21.16 + -9.2x + x2 = -8 + 21.16 Combine like terms: -8 + 21.16 = 13.16 21.16 + -9.2x + x2 = 13.16 Factor a perfect square on the left side: (x + -4.6)(x + -4.6) = 13.16 Calculate the square root of the right side: 3.627671429 Break this problem into two subproblems by setting (x + -4.6) equal to 3.627671429 and -3.627671429.Subproblem 1
x + -4.6 = 3.627671429 Simplifying x + -4.6 = 3.627671429 Reorder the terms: -4.6 + x = 3.627671429 Solving -4.6 + x = 3.627671429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6' to each side of the equation. -4.6 + 4.6 + x = 3.627671429 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x = 3.627671429 + 4.6 x = 3.627671429 + 4.6 Combine like terms: 3.627671429 + 4.6 = 8.227671429 x = 8.227671429 Simplifying x = 8.227671429Subproblem 2
x + -4.6 = -3.627671429 Simplifying x + -4.6 = -3.627671429 Reorder the terms: -4.6 + x = -3.627671429 Solving -4.6 + x = -3.627671429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6' to each side of the equation. -4.6 + 4.6 + x = -3.627671429 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x = -3.627671429 + 4.6 x = -3.627671429 + 4.6 Combine like terms: -3.627671429 + 4.6 = 0.972328571 x = 0.972328571 Simplifying x = 0.972328571Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.227671429, 0.972328571}
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