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Simplifying 4x2 + -6x = 25x + -35 Reorder the terms: -6x + 4x2 = 25x + -35 Reorder the terms: -6x + 4x2 = -35 + 25x Solving -6x + 4x2 = -35 + 25x Solving for variable 'x'. Reorder the terms: 35 + -6x + -25x + 4x2 = -35 + 25x + 35 + -25x Combine like terms: -6x + -25x = -31x 35 + -31x + 4x2 = -35 + 25x + 35 + -25x Reorder the terms: 35 + -31x + 4x2 = -35 + 35 + 25x + -25x Combine like terms: -35 + 35 = 0 35 + -31x + 4x2 = 0 + 25x + -25x 35 + -31x + 4x2 = 25x + -25x Combine like terms: 25x + -25x = 0 35 + -31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.75 + -7.75x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + -7.75x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + -7.75x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + -7.75x + x2 = 0 + -8.75 -7.75x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 -7.75x + x2 = -8.75 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 = -8.75 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = -8.75 + 15.015625 Combine like terms: -8.75 + 15.015625 = 6.265625 15.015625 + -7.75x + x2 = 6.265625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 6.265625 Calculate the square root of the right side: 2.503123049 Break this problem into two subproblems by setting (x + -3.875) equal to 2.503123049 and -2.503123049.Subproblem 1
x + -3.875 = 2.503123049 Simplifying x + -3.875 = 2.503123049 Reorder the terms: -3.875 + x = 2.503123049 Solving -3.875 + x = 2.503123049 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 = 2.503123049 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 2.503123049 + 3.875 x = 2.503123049 + 3.875 Combine like terms: 2.503123049 + 3.875 = 6.378123049 x = 6.378123049 Simplifying x = 6.378123049Subproblem 2
x + -3.875 = -2.503123049 Simplifying x + -3.875 = -2.503123049 Reorder the terms: -3.875 + x = -2.503123049 Solving -3.875 + x = -2.503123049 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 = -2.503123049 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -2.503123049 + 3.875 x = -2.503123049 + 3.875 Combine like terms: -2.503123049 + 3.875 = 1.371876951 x = 1.371876951 Simplifying x = 1.371876951Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.378123049, 1.371876951}
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