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Simplifying 2x(x + -5) = 2x + 1(x + -4) Reorder the terms: 2x(-5 + x) = 2x + 1(x + -4) (-5 * 2x + x * 2x) = 2x + 1(x + -4) (-10x + 2x2) = 2x + 1(x + -4) Reorder the terms: -10x + 2x2 = 2x + 1(-4 + x) -10x + 2x2 = 2x + (-4 * 1 + x * 1) -10x + 2x2 = 2x + (-4 + 1x) Reorder the terms: -10x + 2x2 = -4 + 2x + 1x Combine like terms: 2x + 1x = 3x -10x + 2x2 = -4 + 3x Solving -10x + 2x2 = -4 + 3x Solving for variable 'x'. Reorder the terms: 4 + -10x + -3x + 2x2 = -4 + 3x + 4 + -3x Combine like terms: -10x + -3x = -13x 4 + -13x + 2x2 = -4 + 3x + 4 + -3x Reorder the terms: 4 + -13x + 2x2 = -4 + 4 + 3x + -3x Combine like terms: -4 + 4 = 0 4 + -13x + 2x2 = 0 + 3x + -3x 4 + -13x + 2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 4 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -6.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -6.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6.5x + x2 = 0 + -2 -6.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6.5x + x2 = -2 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -2 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -2 + 10.5625 Combine like terms: -2 + 10.5625 = 8.5625 10.5625 + -6.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + -3.25) equal to 2.926174978 and -2.926174978.Subproblem 1
x + -3.25 = 2.926174978 Simplifying x + -3.25 = 2.926174978 Reorder the terms: -3.25 + x = 2.926174978 Solving -3.25 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.926174978 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.926174978 + 3.25 x = 2.926174978 + 3.25 Combine like terms: 2.926174978 + 3.25 = 6.176174978 x = 6.176174978 Simplifying x = 6.176174978Subproblem 2
x + -3.25 = -2.926174978 Simplifying x + -3.25 = -2.926174978 Reorder the terms: -3.25 + x = -2.926174978 Solving -3.25 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.926174978 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.926174978 + 3.25 x = -2.926174978 + 3.25 Combine like terms: -2.926174978 + 3.25 = 0.323825022 x = 0.323825022 Simplifying x = 0.323825022Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.176174978, 0.323825022}
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