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Simplifying (4x + -2)(5x + -5) = x Reorder the terms: (-2 + 4x)(5x + -5) = x Reorder the terms: (-2 + 4x)(-5 + 5x) = x Multiply (-2 + 4x) * (-5 + 5x) (-2(-5 + 5x) + 4x * (-5 + 5x)) = x ((-5 * -2 + 5x * -2) + 4x * (-5 + 5x)) = x ((10 + -10x) + 4x * (-5 + 5x)) = x (10 + -10x + (-5 * 4x + 5x * 4x)) = x (10 + -10x + (-20x + 20x2)) = x Combine like terms: -10x + -20x = -30x (10 + -30x + 20x2) = x Solving 10 + -30x + 20x2 = x Solving for variable 'x'. Reorder the terms: 10 + -30x + -1x + 20x2 = x + -1x Combine like terms: -30x + -1x = -31x 10 + -31x + 20x2 = x + -1x Combine like terms: x + -1x = 0 10 + -31x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.5 + -1.55x + x2 = 0.0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.55x + -0.5 + x2 = 0.0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.55x + x2 = 0.0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.55x + x2 = 0.0 + -0.5 -1.55x + x2 = 0.0 + -0.5 Combine like terms: 0.0 + -0.5 = -0.5 -1.55x + x2 = -0.5 The x term is -1.55x. Take half its coefficient (-0.775). Square it (0.600625) and add it to both sides. Add '0.600625' to each side of the equation. -1.55x + 0.600625 + x2 = -0.5 + 0.600625 Reorder the terms: 0.600625 + -1.55x + x2 = -0.5 + 0.600625 Combine like terms: -0.5 + 0.600625 = 0.100625 0.600625 + -1.55x + x2 = 0.100625 Factor a perfect square on the left side: (x + -0.775)(x + -0.775) = 0.100625 Calculate the square root of the right side: 0.317214439 Break this problem into two subproblems by setting (x + -0.775) equal to 0.317214439 and -0.317214439.Subproblem 1
x + -0.775 = 0.317214439 Simplifying x + -0.775 = 0.317214439 Reorder the terms: -0.775 + x = 0.317214439 Solving -0.775 + x = 0.317214439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.775' to each side of the equation. -0.775 + 0.775 + x = 0.317214439 + 0.775 Combine like terms: -0.775 + 0.775 = 0.000 0.000 + x = 0.317214439 + 0.775 x = 0.317214439 + 0.775 Combine like terms: 0.317214439 + 0.775 = 1.092214439 x = 1.092214439 Simplifying x = 1.092214439Subproblem 2
x + -0.775 = -0.317214439 Simplifying x + -0.775 = -0.317214439 Reorder the terms: -0.775 + x = -0.317214439 Solving -0.775 + x = -0.317214439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.775' to each side of the equation. -0.775 + 0.775 + x = -0.317214439 + 0.775 Combine like terms: -0.775 + 0.775 = 0.000 0.000 + x = -0.317214439 + 0.775 x = -0.317214439 + 0.775 Combine like terms: -0.317214439 + 0.775 = 0.457785561 x = 0.457785561 Simplifying x = 0.457785561Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.092214439, 0.457785561}
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