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Simplifying 2x(x + -8) = x + 3x + -5 Reorder the terms: 2x(-8 + x) = x + 3x + -5 (-8 * 2x + x * 2x) = x + 3x + -5 (-16x + 2x2) = x + 3x + -5 Reorder the terms: -16x + 2x2 = -5 + x + 3x Combine like terms: x + 3x = 4x -16x + 2x2 = -5 + 4x Solving -16x + 2x2 = -5 + 4x Solving for variable 'x'. Reorder the terms: 5 + -16x + -4x + 2x2 = -5 + 4x + 5 + -4x Combine like terms: -16x + -4x = -20x 5 + -20x + 2x2 = -5 + 4x + 5 + -4x Reorder the terms: 5 + -20x + 2x2 = -5 + 5 + 4x + -4x Combine like terms: -5 + 5 = 0 5 + -20x + 2x2 = 0 + 4x + -4x 5 + -20x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 5 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -10x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -10x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -10x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -10x + x2 = 0 + -2.5 -10x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -10x + x2 = -2.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -2.5 + 25 Reorder the terms: 25 + -10x + x2 = -2.5 + 25 Combine like terms: -2.5 + 25 = 22.5 25 + -10x + x2 = 22.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + -5) equal to 4.74341649 and -4.74341649.Subproblem 1
x + -5 = 4.74341649 Simplifying x + -5 = 4.74341649 Reorder the terms: -5 + x = 4.74341649 Solving -5 + x = 4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.74341649 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.74341649 + 5 x = 4.74341649 + 5 Combine like terms: 4.74341649 + 5 = 9.74341649 x = 9.74341649 Simplifying x = 9.74341649Subproblem 2
x + -5 = -4.74341649 Simplifying x + -5 = -4.74341649 Reorder the terms: -5 + x = -4.74341649 Solving -5 + x = -4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.74341649 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.74341649 + 5 x = -4.74341649 + 5 Combine like terms: -4.74341649 + 5 = 0.25658351 x = 0.25658351 Simplifying x = 0.25658351Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.74341649, 0.25658351}
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