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Simplifying 8x2 + 33x + 15 = 0 Reorder the terms: 15 + 33x + 8x2 = 0 Solving 15 + 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'. 1.875 + 4.125x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + 4.125x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + 4.125x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + 4.125x + x2 = 0 + -1.875 4.125x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 4.125x + x2 = -1.875 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 = -1.875 + 4.25390625 Reorder the terms: 4.25390625 + 4.125x + x2 = -1.875 + 4.25390625 Combine like terms: -1.875 + 4.25390625 = 2.37890625 4.25390625 + 4.125x + x2 = 2.37890625 Factor a perfect square on the left side: (x + 2.0625)(x + 2.0625) = 2.37890625 Calculate the square root of the right side: 1.542370335 Break this problem into two subproblems by setting (x + 2.0625) equal to 1.542370335 and -1.542370335.Subproblem 1
x + 2.0625 = 1.542370335 Simplifying x + 2.0625 = 1.542370335 Reorder the terms: 2.0625 + x = 1.542370335 Solving 2.0625 + x = 1.542370335 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 = 1.542370335 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + x = 1.542370335 + -2.0625 x = 1.542370335 + -2.0625 Combine like terms: 1.542370335 + -2.0625 = -0.520129665 x = -0.520129665 Simplifying x = -0.520129665Subproblem 2
x + 2.0625 = -1.542370335 Simplifying x + 2.0625 = -1.542370335 Reorder the terms: 2.0625 + x = -1.542370335 Solving 2.0625 + x = -1.542370335 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 = -1.542370335 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + x = -1.542370335 + -2.0625 x = -1.542370335 + -2.0625 Combine like terms: -1.542370335 + -2.0625 = -3.604870335 x = -3.604870335 Simplifying x = -3.604870335Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.520129665, -3.604870335}
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