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Simplifying (5x + -5)(x + -8) = -34 + 76 Reorder the terms: (-5 + 5x)(x + -8) = -34 + 76 Reorder the terms: (-5 + 5x)(-8 + x) = -34 + 76 Multiply (-5 + 5x) * (-8 + x) (-5(-8 + x) + 5x * (-8 + x)) = -34 + 76 ((-8 * -5 + x * -5) + 5x * (-8 + x)) = -34 + 76 ((40 + -5x) + 5x * (-8 + x)) = -34 + 76 (40 + -5x + (-8 * 5x + x * 5x)) = -34 + 76 (40 + -5x + (-40x + 5x2)) = -34 + 76 Combine like terms: -5x + -40x = -45x (40 + -45x + 5x2) = -34 + 76 Combine like terms: -34 + 76 = 42 40 + -45x + 5x2 = 42 Solving 40 + -45x + 5x2 = 42 Solving for variable 'x'. Reorder the terms: 40 + -42 + -45x + 5x2 = 42 + -42 Combine like terms: 40 + -42 = -2 -2 + -45x + 5x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -2 + -45x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -9x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -9x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -9x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -9x + x2 = 0 + 0.4 -9x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -9x + x2 = 0.4 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 0.4 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 0.4 + 20.25 Combine like terms: 0.4 + 20.25 = 20.65 20.25 + -9x + x2 = 20.65 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 20.65 Calculate the square root of the right side: 4.544227107 Break this problem into two subproblems by setting (x + -4.5) equal to 4.544227107 and -4.544227107.Subproblem 1
x + -4.5 = 4.544227107 Simplifying x + -4.5 = 4.544227107 Reorder the terms: -4.5 + x = 4.544227107 Solving -4.5 + x = 4.544227107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.544227107 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.544227107 + 4.5 x = 4.544227107 + 4.5 Combine like terms: 4.544227107 + 4.5 = 9.044227107 x = 9.044227107 Simplifying x = 9.044227107Subproblem 2
x + -4.5 = -4.544227107 Simplifying x + -4.5 = -4.544227107 Reorder the terms: -4.5 + x = -4.544227107 Solving -4.5 + x = -4.544227107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.544227107 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.544227107 + 4.5 x = -4.544227107 + 4.5 Combine like terms: -4.544227107 + 4.5 = -0.044227107 x = -0.044227107 Simplifying x = -0.044227107Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.044227107, -0.044227107}
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