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Simplifying 8x2 + -33x + 12 = 0 Reorder the terms: 12 + -33x + 8x2 = 0 Solving 12 + -33x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + -4.125x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4.125x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4.125x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4.125x + x2 = 0 + -1.5 -4.125x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4.125x + x2 = -1.5 The x term is -4.125x. Take half its coefficient (-2.0625). Square it (4.25390625) and add it to both sides. Add '4.25390625' to each side of the equation. -4.125x + 4.25390625 + x2 = -1.5 + 4.25390625 Reorder the terms: 4.25390625 + -4.125x + x2 = -1.5 + 4.25390625 Combine like terms: -1.5 + 4.25390625 = 2.75390625 4.25390625 + -4.125x + x2 = 2.75390625 Factor a perfect square on the left side: (x + -2.0625)(x + -2.0625) = 2.75390625 Calculate the square root of the right side: 1.659489756 Break this problem into two subproblems by setting (x + -2.0625) equal to 1.659489756 and -1.659489756.Subproblem 1
x + -2.0625 = 1.659489756 Simplifying x + -2.0625 = 1.659489756 Reorder the terms: -2.0625 + x = 1.659489756 Solving -2.0625 + x = 1.659489756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = 1.659489756 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = 1.659489756 + 2.0625 x = 1.659489756 + 2.0625 Combine like terms: 1.659489756 + 2.0625 = 3.721989756 x = 3.721989756 Simplifying x = 3.721989756Subproblem 2
x + -2.0625 = -1.659489756 Simplifying x + -2.0625 = -1.659489756 Reorder the terms: -2.0625 + x = -1.659489756 Solving -2.0625 + x = -1.659489756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = -1.659489756 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = -1.659489756 + 2.0625 x = -1.659489756 + 2.0625 Combine like terms: -1.659489756 + 2.0625 = 0.403010244 x = 0.403010244 Simplifying x = 0.403010244Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.721989756, 0.403010244}
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