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Simplifying 8x2 + 33x + -4 = 0 Reorder the terms: -4 + 33x + 8x2 = 0 Solving -4 + 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'. -0.5 + 4.125x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 4.125x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 4.125x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 4.125x + x2 = 0 + 0.5 4.125x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 4.125x + x2 = 0.5 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 = 0.5 + 4.25390625 Reorder the terms: 4.25390625 + 4.125x + x2 = 0.5 + 4.25390625 Combine like terms: 0.5 + 4.25390625 = 4.75390625 4.25390625 + 4.125x + x2 = 4.75390625 Factor a perfect square on the left side: (x + 2.0625)(x + 2.0625) = 4.75390625 Calculate the square root of the right side: 2.180345443 Break this problem into two subproblems by setting (x + 2.0625) equal to 2.180345443 and -2.180345443.Subproblem 1
x + 2.0625 = 2.180345443 Simplifying x + 2.0625 = 2.180345443 Reorder the terms: 2.0625 + x = 2.180345443 Solving 2.0625 + x = 2.180345443 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 = 2.180345443 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + x = 2.180345443 + -2.0625 x = 2.180345443 + -2.0625 Combine like terms: 2.180345443 + -2.0625 = 0.117845443 x = 0.117845443 Simplifying x = 0.117845443Subproblem 2
x + 2.0625 = -2.180345443 Simplifying x + 2.0625 = -2.180345443 Reorder the terms: 2.0625 + x = -2.180345443 Solving 2.0625 + x = -2.180345443 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 = -2.180345443 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + x = -2.180345443 + -2.0625 x = -2.180345443 + -2.0625 Combine like terms: -2.180345443 + -2.0625 = -4.242845443 x = -4.242845443 Simplifying x = -4.242845443Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.117845443, -4.242845443}
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