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Simplifying (2x + -5)(5x + -5) = 56 Reorder the terms: (-5 + 2x)(5x + -5) = 56 Reorder the terms: (-5 + 2x)(-5 + 5x) = 56 Multiply (-5 + 2x) * (-5 + 5x) (-5(-5 + 5x) + 2x * (-5 + 5x)) = 56 ((-5 * -5 + 5x * -5) + 2x * (-5 + 5x)) = 56 ((25 + -25x) + 2x * (-5 + 5x)) = 56 (25 + -25x + (-5 * 2x + 5x * 2x)) = 56 (25 + -25x + (-10x + 10x2)) = 56 Combine like terms: -25x + -10x = -35x (25 + -35x + 10x2) = 56 Solving 25 + -35x + 10x2 = 56 Solving for variable 'x'. Reorder the terms: 25 + -56 + -35x + 10x2 = 56 + -56 Combine like terms: 25 + -56 = -31 -31 + -35x + 10x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -31 + -35x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.1 + -3.5x + x2 = 0.0 Move the constant term to the right: Add '3.1' to each side of the equation. -3.1 + -3.5x + 3.1 + x2 = 0.0 + 3.1 Reorder the terms: -3.1 + 3.1 + -3.5x + x2 = 0.0 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + -3.5x + x2 = 0.0 + 3.1 -3.5x + x2 = 0.0 + 3.1 Combine like terms: 0.0 + 3.1 = 3.1 -3.5x + x2 = 3.1 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 3.1 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 3.1 + 3.0625 Combine like terms: 3.1 + 3.0625 = 6.1625 3.0625 + -3.5x + x2 = 6.1625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 6.1625 Calculate the square root of the right side: 2.482438317 Break this problem into two subproblems by setting (x + -1.75) equal to 2.482438317 and -2.482438317.Subproblem 1
x + -1.75 = 2.482438317 Simplifying x + -1.75 = 2.482438317 Reorder the terms: -1.75 + x = 2.482438317 Solving -1.75 + x = 2.482438317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.482438317 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.482438317 + 1.75 x = 2.482438317 + 1.75 Combine like terms: 2.482438317 + 1.75 = 4.232438317 x = 4.232438317 Simplifying x = 4.232438317Subproblem 2
x + -1.75 = -2.482438317 Simplifying x + -1.75 = -2.482438317 Reorder the terms: -1.75 + x = -2.482438317 Solving -1.75 + x = -2.482438317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.482438317 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.482438317 + 1.75 x = -2.482438317 + 1.75 Combine like terms: -2.482438317 + 1.75 = -0.732438317 x = -0.732438317 Simplifying x = -0.732438317Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.232438317, -0.732438317}
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