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Simplifying 8x2 + -33x + -6 = 0 Reorder the terms: -6 + -33x + 8x2 = 0 Solving -6 + -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'. -0.75 + -4.125x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -4.125x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -4.125x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -4.125x + x2 = 0 + 0.75 -4.125x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -4.125x + x2 = 0.75 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 = 0.75 + 4.25390625 Reorder the terms: 4.25390625 + -4.125x + x2 = 0.75 + 4.25390625 Combine like terms: 0.75 + 4.25390625 = 5.00390625 4.25390625 + -4.125x + x2 = 5.00390625 Factor a perfect square on the left side: (x + -2.0625)(x + -2.0625) = 5.00390625 Calculate the square root of the right side: 2.236941271 Break this problem into two subproblems by setting (x + -2.0625) equal to 2.236941271 and -2.236941271.Subproblem 1
x + -2.0625 = 2.236941271 Simplifying x + -2.0625 = 2.236941271 Reorder the terms: -2.0625 + x = 2.236941271 Solving -2.0625 + x = 2.236941271 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 = 2.236941271 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = 2.236941271 + 2.0625 x = 2.236941271 + 2.0625 Combine like terms: 2.236941271 + 2.0625 = 4.299441271 x = 4.299441271 Simplifying x = 4.299441271Subproblem 2
x + -2.0625 = -2.236941271 Simplifying x + -2.0625 = -2.236941271 Reorder the terms: -2.0625 + x = -2.236941271 Solving -2.0625 + x = -2.236941271 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 = -2.236941271 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = -2.236941271 + 2.0625 x = -2.236941271 + 2.0625 Combine like terms: -2.236941271 + 2.0625 = -0.174441271 x = -0.174441271 Simplifying x = -0.174441271Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.299441271, -0.174441271}
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