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Simplifying 8x2 + -27x + 18 = 0 Reorder the terms: 18 + -27x + 8x2 = 0 Solving 18 + -27x + 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'. 2.25 + -3.375x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -3.375x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -3.375x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -3.375x + x2 = 0 + -2.25 -3.375x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -3.375x + x2 = -2.25 The x term is -3.375x. Take half its coefficient (-1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. -3.375x + 2.84765625 + x2 = -2.25 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = -2.25 + 2.84765625 Combine like terms: -2.25 + 2.84765625 = 0.59765625 2.84765625 + -3.375x + x2 = 0.59765625 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = 0.59765625 Calculate the square root of the right side: 0.773082305 Break this problem into two subproblems by setting (x + -1.6875) equal to 0.773082305 and -0.773082305.Subproblem 1
x + -1.6875 = 0.773082305 Simplifying x + -1.6875 = 0.773082305 Reorder the terms: -1.6875 + x = 0.773082305 Solving -1.6875 + x = 0.773082305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = 0.773082305 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 0.773082305 + 1.6875 x = 0.773082305 + 1.6875 Combine like terms: 0.773082305 + 1.6875 = 2.460582305 x = 2.460582305 Simplifying x = 2.460582305Subproblem 2
x + -1.6875 = -0.773082305 Simplifying x + -1.6875 = -0.773082305 Reorder the terms: -1.6875 + x = -0.773082305 Solving -1.6875 + x = -0.773082305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = -0.773082305 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -0.773082305 + 1.6875 x = -0.773082305 + 1.6875 Combine like terms: -0.773082305 + 1.6875 = 0.914417695 x = 0.914417695 Simplifying x = 0.914417695Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.460582305, 0.914417695}
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