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Simplifying 4x2 + -33x = 8 Reorder the terms: -33x + 4x2 = 8 Solving -33x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -33x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -33x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -8.25x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -8.25x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -8.25x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -8.25x + x2 = 0 + 2 -8.25x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -8.25x + x2 = 2 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = 2 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = 2 + 17.015625 Combine like terms: 2 + 17.015625 = 19.015625 17.015625 + -8.25x + x2 = 19.015625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 19.015625 Calculate the square root of the right side: 4.360690886 Break this problem into two subproblems by setting (x + -4.125) equal to 4.360690886 and -4.360690886.Subproblem 1
x + -4.125 = 4.360690886 Simplifying x + -4.125 = 4.360690886 Reorder the terms: -4.125 + x = 4.360690886 Solving -4.125 + x = 4.360690886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = 4.360690886 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 4.360690886 + 4.125 x = 4.360690886 + 4.125 Combine like terms: 4.360690886 + 4.125 = 8.485690886 x = 8.485690886 Simplifying x = 8.485690886Subproblem 2
x + -4.125 = -4.360690886 Simplifying x + -4.125 = -4.360690886 Reorder the terms: -4.125 + x = -4.360690886 Solving -4.125 + x = -4.360690886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = -4.360690886 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -4.360690886 + 4.125 x = -4.360690886 + 4.125 Combine like terms: -4.360690886 + 4.125 = -0.235690886 x = -0.235690886 Simplifying x = -0.235690886Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.485690886, -0.235690886}
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