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Simplifying 8 + (5x + -6 + -4x + 1) = x(x + -4) Reorder the terms: 8 + (-6 + 1 + 5x + -4x) = x(x + -4) Combine like terms: -6 + 1 = -5 8 + (-5 + 5x + -4x) = x(x + -4) Combine like terms: 5x + -4x = 1x 8 + (-5 + 1x) = x(x + -4) Remove parenthesis around (-5 + 1x) 8 + -5 + 1x = x(x + -4) Combine like terms: 8 + -5 = 3 3 + 1x = x(x + -4) Reorder the terms: 3 + 1x = x(-4 + x) 3 + 1x = (-4 * x + x * x) 3 + 1x = (-4x + x2) Solving 3 + 1x = -4x + x2 Solving for variable 'x'. Combine like terms: 1x + 4x = 5x 3 + 5x + -1x2 = -4x + x2 + 4x + -1x2 Reorder the terms: 3 + 5x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 3 + 5x + -1x2 = 0 + x2 + -1x2 3 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5x + x2 = 0 + 3 -5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5x + x2 = 3 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 3 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + -5x + x2 = 9.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -2.5 = 3.041381265 Simplifying x + -2.5 = 3.041381265 Reorder the terms: -2.5 + x = 3.041381265 Solving -2.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.041381265 + 2.5 x = 3.041381265 + 2.5 Combine like terms: 3.041381265 + 2.5 = 5.541381265 x = 5.541381265 Simplifying x = 5.541381265Subproblem 2
x + -2.5 = -3.041381265 Simplifying x + -2.5 = -3.041381265 Reorder the terms: -2.5 + x = -3.041381265 Solving -2.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.041381265 + 2.5 x = -3.041381265 + 2.5 Combine like terms: -3.041381265 + 2.5 = -0.541381265 x = -0.541381265 Simplifying x = -0.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.541381265, -0.541381265}
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