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Simplifying (x + -5)(4x + -10) = x Reorder the terms: (-5 + x)(4x + -10) = x Reorder the terms: (-5 + x)(-10 + 4x) = x Multiply (-5 + x) * (-10 + 4x) (-5(-10 + 4x) + x(-10 + 4x)) = x ((-10 * -5 + 4x * -5) + x(-10 + 4x)) = x ((50 + -20x) + x(-10 + 4x)) = x (50 + -20x + (-10 * x + 4x * x)) = x (50 + -20x + (-10x + 4x2)) = x Combine like terms: -20x + -10x = -30x (50 + -30x + 4x2) = x Solving 50 + -30x + 4x2 = x Solving for variable 'x'. Reorder the terms: 50 + -30x + -1x + 4x2 = x + -1x Combine like terms: -30x + -1x = -31x 50 + -31x + 4x2 = x + -1x Combine like terms: x + -1x = 0 50 + -31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.5 + -7.75x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -7.75x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -7.75x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -7.75x + x2 = 0 + -12.5 -7.75x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -7.75x + x2 = -12.5 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = -12.5 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = -12.5 + 15.015625 Combine like terms: -12.5 + 15.015625 = 2.515625 15.015625 + -7.75x + x2 = 2.515625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + -3.875) equal to 1.586072193 and -1.586072193.Subproblem 1
x + -3.875 = 1.586072193 Simplifying x + -3.875 = 1.586072193 Reorder the terms: -3.875 + x = 1.586072193 Solving -3.875 + x = 1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 1.586072193 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 1.586072193 + 3.875 x = 1.586072193 + 3.875 Combine like terms: 1.586072193 + 3.875 = 5.461072193 x = 5.461072193 Simplifying x = 5.461072193Subproblem 2
x + -3.875 = -1.586072193 Simplifying x + -3.875 = -1.586072193 Reorder the terms: -3.875 + x = -1.586072193 Solving -3.875 + x = -1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -1.586072193 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -1.586072193 + 3.875 x = -1.586072193 + 3.875 Combine like terms: -1.586072193 + 3.875 = 2.288927807 x = 2.288927807 Simplifying x = 2.288927807Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.461072193, 2.288927807}
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