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Simplifying 4x + 5(x + -8) = 4x(x + -5) Reorder the terms: 4x + 5(-8 + x) = 4x(x + -5) 4x + (-8 * 5 + x * 5) = 4x(x + -5) 4x + (-40 + 5x) = 4x(x + -5) Reorder the terms: -40 + 4x + 5x = 4x(x + -5) Combine like terms: 4x + 5x = 9x -40 + 9x = 4x(x + -5) Reorder the terms: -40 + 9x = 4x(-5 + x) -40 + 9x = (-5 * 4x + x * 4x) -40 + 9x = (-20x + 4x2) Solving -40 + 9x = -20x + 4x2 Solving for variable 'x'. Combine like terms: 9x + 20x = 29x -40 + 29x + -4x2 = -20x + 4x2 + 20x + -4x2 Reorder the terms: -40 + 29x + -4x2 = -20x + 20x + 4x2 + -4x2 Combine like terms: -20x + 20x = 0 -40 + 29x + -4x2 = 0 + 4x2 + -4x2 -40 + 29x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -40 + 29x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 10 + -7.25x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -7.25x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -7.25x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7.25x + x2 = 0 + -10 -7.25x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -7.25x + x2 = -10 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = -10 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -10 + 13.140625 Combine like terms: -10 + 13.140625 = 3.140625 13.140625 + -7.25x + x2 = 3.140625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + -3.625) equal to 1.77218086 and -1.77218086.Subproblem 1
x + -3.625 = 1.77218086 Simplifying x + -3.625 = 1.77218086 Reorder the terms: -3.625 + x = 1.77218086 Solving -3.625 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 1.77218086 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 1.77218086 + 3.625 x = 1.77218086 + 3.625 Combine like terms: 1.77218086 + 3.625 = 5.39718086 x = 5.39718086 Simplifying x = 5.39718086Subproblem 2
x + -3.625 = -1.77218086 Simplifying x + -3.625 = -1.77218086 Reorder the terms: -3.625 + x = -1.77218086 Solving -3.625 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -1.77218086 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -1.77218086 + 3.625 x = -1.77218086 + 3.625 Combine like terms: -1.77218086 + 3.625 = 1.85281914 x = 1.85281914 Simplifying x = 1.85281914Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.39718086, 1.85281914}
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