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Simplifying 4x2 + -36x + -6 = 2x2 + -1x Reorder the terms: -6 + -36x + 4x2 = 2x2 + -1x Reorder the terms: -6 + -36x + 4x2 = -1x + 2x2 Solving -6 + -36x + 4x2 = -1x + 2x2 Solving for variable 'x'. Reorder the terms: -6 + -36x + x + 4x2 + -2x2 = -1x + 2x2 + x + -2x2 Combine like terms: -36x + x = -35x -6 + -35x + 4x2 + -2x2 = -1x + 2x2 + x + -2x2 Combine like terms: 4x2 + -2x2 = 2x2 -6 + -35x + 2x2 = -1x + 2x2 + x + -2x2 Reorder the terms: -6 + -35x + 2x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 -6 + -35x + 2x2 = 0 + 2x2 + -2x2 -6 + -35x + 2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + -35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -17.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -17.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -17.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -17.5x + x2 = 0 + 3 -17.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -17.5x + x2 = 3 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = 3 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = 3 + 76.5625 Combine like terms: 3 + 76.5625 = 79.5625 76.5625 + -17.5x + x2 = 79.5625 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 79.5625 Calculate the square root of the right side: 8.919781387 Break this problem into two subproblems by setting (x + -8.75) equal to 8.919781387 and -8.919781387.Subproblem 1
x + -8.75 = 8.919781387 Simplifying x + -8.75 = 8.919781387 Reorder the terms: -8.75 + x = 8.919781387 Solving -8.75 + x = 8.919781387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 8.919781387 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 8.919781387 + 8.75 x = 8.919781387 + 8.75 Combine like terms: 8.919781387 + 8.75 = 17.669781387 x = 17.669781387 Simplifying x = 17.669781387Subproblem 2
x + -8.75 = -8.919781387 Simplifying x + -8.75 = -8.919781387 Reorder the terms: -8.75 + x = -8.919781387 Solving -8.75 + x = -8.919781387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -8.919781387 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -8.919781387 + 8.75 x = -8.919781387 + 8.75 Combine like terms: -8.919781387 + 8.75 = -0.169781387 x = -0.169781387 Simplifying x = -0.169781387Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.669781387, -0.169781387}
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