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Simplifying 5(2x + -1) = 4x(x + -15) Reorder the terms: 5(-1 + 2x) = 4x(x + -15) (-1 * 5 + 2x * 5) = 4x(x + -15) (-5 + 10x) = 4x(x + -15) Reorder the terms: -5 + 10x = 4x(-15 + x) -5 + 10x = (-15 * 4x + x * 4x) -5 + 10x = (-60x + 4x2) Solving -5 + 10x = -60x + 4x2 Solving for variable 'x'. Combine like terms: 10x + 60x = 70x -5 + 70x + -4x2 = -60x + 4x2 + 60x + -4x2 Reorder the terms: -5 + 70x + -4x2 = -60x + 60x + 4x2 + -4x2 Combine like terms: -60x + 60x = 0 -5 + 70x + -4x2 = 0 + 4x2 + -4x2 -5 + 70x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + 70x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -17.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -17.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -17.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -17.5x + x2 = 0 + -1.25 -17.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -17.5x + x2 = -1.25 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = -1.25 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = -1.25 + 76.5625 Combine like terms: -1.25 + 76.5625 = 75.3125 76.5625 + -17.5x + x2 = 75.3125 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 75.3125 Calculate the square root of the right side: 8.678277479 Break this problem into two subproblems by setting (x + -8.75) equal to 8.678277479 and -8.678277479.Subproblem 1
x + -8.75 = 8.678277479 Simplifying x + -8.75 = 8.678277479 Reorder the terms: -8.75 + x = 8.678277479 Solving -8.75 + x = 8.678277479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 8.678277479 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 8.678277479 + 8.75 x = 8.678277479 + 8.75 Combine like terms: 8.678277479 + 8.75 = 17.428277479 x = 17.428277479 Simplifying x = 17.428277479Subproblem 2
x + -8.75 = -8.678277479 Simplifying x + -8.75 = -8.678277479 Reorder the terms: -8.75 + x = -8.678277479 Solving -8.75 + x = -8.678277479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -8.678277479 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -8.678277479 + 8.75 x = -8.678277479 + 8.75 Combine like terms: -8.678277479 + 8.75 = 0.071722521 x = 0.071722521 Simplifying x = 0.071722521Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.428277479, 0.071722521}
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