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Simplifying 8x2 + 33x + 14 = 0 Reorder the terms: 14 + 33x + 8x2 = 0 Solving 14 + 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'. 1.75 + 4.125x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 4.125x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 4.125x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 4.125x + x2 = 0 + -1.75 4.125x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 4.125x + x2 = -1.75 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 = -1.75 + 4.25390625 Reorder the terms: 4.25390625 + 4.125x + x2 = -1.75 + 4.25390625 Combine like terms: -1.75 + 4.25390625 = 2.50390625 4.25390625 + 4.125x + x2 = 2.50390625 Factor a perfect square on the left side: (x + 2.0625)(x + 2.0625) = 2.50390625 Calculate the square root of the right side: 1.582373613 Break this problem into two subproblems by setting (x + 2.0625) equal to 1.582373613 and -1.582373613.Subproblem 1
x + 2.0625 = 1.582373613 Simplifying x + 2.0625 = 1.582373613 Reorder the terms: 2.0625 + x = 1.582373613 Solving 2.0625 + x = 1.582373613 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 = 1.582373613 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + x = 1.582373613 + -2.0625 x = 1.582373613 + -2.0625 Combine like terms: 1.582373613 + -2.0625 = -0.480126387 x = -0.480126387 Simplifying x = -0.480126387Subproblem 2
x + 2.0625 = -1.582373613 Simplifying x + 2.0625 = -1.582373613 Reorder the terms: 2.0625 + x = -1.582373613 Solving 2.0625 + x = -1.582373613 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 = -1.582373613 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + x = -1.582373613 + -2.0625 x = -1.582373613 + -2.0625 Combine like terms: -1.582373613 + -2.0625 = -3.644873613 x = -3.644873613 Simplifying x = -3.644873613Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.480126387, -3.644873613}
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