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Simplifying 3x + 4x(x + -5) = 5x + 8 Reorder the terms: 3x + 4x(-5 + x) = 5x + 8 3x + (-5 * 4x + x * 4x) = 5x + 8 3x + (-20x + 4x2) = 5x + 8 Combine like terms: 3x + -20x = -17x -17x + 4x2 = 5x + 8 Reorder the terms: -17x + 4x2 = 8 + 5x Solving -17x + 4x2 = 8 + 5x Solving for variable 'x'. Reorder the terms: -8 + -17x + -5x + 4x2 = 8 + 5x + -8 + -5x Combine like terms: -17x + -5x = -22x -8 + -22x + 4x2 = 8 + 5x + -8 + -5x Reorder the terms: -8 + -22x + 4x2 = 8 + -8 + 5x + -5x Combine like terms: 8 + -8 = 0 -8 + -22x + 4x2 = 0 + 5x + -5x -8 + -22x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -8 + -22x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -11x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + -11x + 2x2 = 0 Solving -4 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -5.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -5.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -5.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5.5x + x2 = 0 + 2 -5.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5.5x + x2 = 2 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 2 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 2 + 7.5625 Combine like terms: 2 + 7.5625 = 9.5625 7.5625 + -5.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + -2.75) equal to 3.092329219 and -3.092329219.Subproblem 1
x + -2.75 = 3.092329219 Simplifying x + -2.75 = 3.092329219 Reorder the terms: -2.75 + x = 3.092329219 Solving -2.75 + x = 3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.092329219 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.092329219 + 2.75 x = 3.092329219 + 2.75 Combine like terms: 3.092329219 + 2.75 = 5.842329219 x = 5.842329219 Simplifying x = 5.842329219Subproblem 2
x + -2.75 = -3.092329219 Simplifying x + -2.75 = -3.092329219 Reorder the terms: -2.75 + x = -3.092329219 Solving -2.75 + x = -3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.092329219 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.092329219 + 2.75 x = -3.092329219 + 2.75 Combine like terms: -3.092329219 + 2.75 = -0.342329219 x = -0.342329219 Simplifying x = -0.342329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.842329219, -0.342329219}Solution
x = {5.842329219, -0.342329219}
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