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Simplifying 4(x + -4) * x = 5(x + -4) + 4 Reorder the terms: 4(-4 + x) * x = 5(x + -4) + 4 Reorder the terms for easier multiplication: 4x(-4 + x) = 5(x + -4) + 4 (-4 * 4x + x * 4x) = 5(x + -4) + 4 (-16x + 4x2) = 5(x + -4) + 4 Reorder the terms: -16x + 4x2 = 5(-4 + x) + 4 -16x + 4x2 = (-4 * 5 + x * 5) + 4 -16x + 4x2 = (-20 + 5x) + 4 Reorder the terms: -16x + 4x2 = -20 + 4 + 5x Combine like terms: -20 + 4 = -16 -16x + 4x2 = -16 + 5x Solving -16x + 4x2 = -16 + 5x Solving for variable 'x'. Reorder the terms: 16 + -16x + -5x + 4x2 = -16 + 5x + 16 + -5x Combine like terms: -16x + -5x = -21x 16 + -21x + 4x2 = -16 + 5x + 16 + -5x Reorder the terms: 16 + -21x + 4x2 = -16 + 16 + 5x + -5x Combine like terms: -16 + 16 = 0 16 + -21x + 4x2 = 0 + 5x + -5x 16 + -21x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 16 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4 + -5.25x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -5.25x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -5.25x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5.25x + x2 = 0 + -4 -5.25x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5.25x + x2 = -4 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -4 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -4 + 6.890625 Combine like terms: -4 + 6.890625 = 2.890625 6.890625 + -5.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + -2.625) equal to 1.700183814 and -1.700183814.Subproblem 1
x + -2.625 = 1.700183814 Simplifying x + -2.625 = 1.700183814 Reorder the terms: -2.625 + x = 1.700183814 Solving -2.625 + x = 1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 1.700183814 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 1.700183814 + 2.625 x = 1.700183814 + 2.625 Combine like terms: 1.700183814 + 2.625 = 4.325183814 x = 4.325183814 Simplifying x = 4.325183814Subproblem 2
x + -2.625 = -1.700183814 Simplifying x + -2.625 = -1.700183814 Reorder the terms: -2.625 + x = -1.700183814 Solving -2.625 + x = -1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -1.700183814 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -1.700183814 + 2.625 x = -1.700183814 + 2.625 Combine like terms: -1.700183814 + 2.625 = 0.924816186 x = 0.924816186 Simplifying x = 0.924816186Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.325183814, 0.924816186}
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