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Simplifying (4x + -5)(x + -5) = 40 Reorder the terms: (-5 + 4x)(x + -5) = 40 Reorder the terms: (-5 + 4x)(-5 + x) = 40 Multiply (-5 + 4x) * (-5 + x) (-5(-5 + x) + 4x * (-5 + x)) = 40 ((-5 * -5 + x * -5) + 4x * (-5 + x)) = 40 ((25 + -5x) + 4x * (-5 + x)) = 40 (25 + -5x + (-5 * 4x + x * 4x)) = 40 (25 + -5x + (-20x + 4x2)) = 40 Combine like terms: -5x + -20x = -25x (25 + -25x + 4x2) = 40 Solving 25 + -25x + 4x2 = 40 Solving for variable 'x'. Reorder the terms: 25 + -40 + -25x + 4x2 = 40 + -40 Combine like terms: 25 + -40 = -15 -15 + -25x + 4x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -15 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -6.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -6.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -6.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -6.25x + x2 = 0 + 3.75 -6.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -6.25x + x2 = 3.75 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 3.75 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 3.75 + 9.765625 Combine like terms: 3.75 + 9.765625 = 13.515625 9.765625 + -6.25x + x2 = 13.515625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 13.515625 Calculate the square root of the right side: 3.676360292 Break this problem into two subproblems by setting (x + -3.125) equal to 3.676360292 and -3.676360292.Subproblem 1
x + -3.125 = 3.676360292 Simplifying x + -3.125 = 3.676360292 Reorder the terms: -3.125 + x = 3.676360292 Solving -3.125 + x = 3.676360292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.676360292 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.676360292 + 3.125 x = 3.676360292 + 3.125 Combine like terms: 3.676360292 + 3.125 = 6.801360292 x = 6.801360292 Simplifying x = 6.801360292Subproblem 2
x + -3.125 = -3.676360292 Simplifying x + -3.125 = -3.676360292 Reorder the terms: -3.125 + x = -3.676360292 Solving -3.125 + x = -3.676360292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.676360292 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.676360292 + 3.125 x = -3.676360292 + 3.125 Combine like terms: -3.676360292 + 3.125 = -0.551360292 x = -0.551360292 Simplifying x = -0.551360292Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.801360292, -0.551360292}
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