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Simplifying 8x2 + -33x + -39 = x Reorder the terms: -39 + -33x + 8x2 = x Solving -39 + -33x + 8x2 = x Solving for variable 'x'. Reorder the terms: -39 + -33x + -1x + 8x2 = x + -1x Combine like terms: -33x + -1x = -34x -39 + -34x + 8x2 = x + -1x Combine like terms: x + -1x = 0 -39 + -34x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.875 + -4.25x + x2 = 0 Move the constant term to the right: Add '4.875' to each side of the equation. -4.875 + -4.25x + 4.875 + x2 = 0 + 4.875 Reorder the terms: -4.875 + 4.875 + -4.25x + x2 = 0 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + -4.25x + x2 = 0 + 4.875 -4.25x + x2 = 0 + 4.875 Combine like terms: 0 + 4.875 = 4.875 -4.25x + x2 = 4.875 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 4.875 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 4.875 + 4.515625 Combine like terms: 4.875 + 4.515625 = 9.390625 4.515625 + -4.25x + x2 = 9.390625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 9.390625 Calculate the square root of the right side: 3.064412668 Break this problem into two subproblems by setting (x + -2.125) equal to 3.064412668 and -3.064412668.Subproblem 1
x + -2.125 = 3.064412668 Simplifying x + -2.125 = 3.064412668 Reorder the terms: -2.125 + x = 3.064412668 Solving -2.125 + x = 3.064412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 3.064412668 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 3.064412668 + 2.125 x = 3.064412668 + 2.125 Combine like terms: 3.064412668 + 2.125 = 5.189412668 x = 5.189412668 Simplifying x = 5.189412668Subproblem 2
x + -2.125 = -3.064412668 Simplifying x + -2.125 = -3.064412668 Reorder the terms: -2.125 + x = -3.064412668 Solving -2.125 + x = -3.064412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -3.064412668 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -3.064412668 + 2.125 x = -3.064412668 + 2.125 Combine like terms: -3.064412668 + 2.125 = -0.939412668 x = -0.939412668 Simplifying x = -0.939412668Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.189412668, -0.939412668}
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