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Simplifying 3x2 + -81x + -7 = 0 Reorder the terms: -7 + -81x + 3x2 = 0 Solving -7 + -81x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -27x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -27x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -27x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -27x + x2 = 0 + 2.333333333 -27x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -27x + x2 = 2.333333333 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = 2.333333333 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 2.333333333 + 182.25 Combine like terms: 2.333333333 + 182.25 = 184.583333333 182.25 + -27x + x2 = 184.583333333 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 184.583333333 Calculate the square root of the right side: 13.586144903 Break this problem into two subproblems by setting (x + -13.5) equal to 13.586144903 and -13.586144903.Subproblem 1
x + -13.5 = 13.586144903 Simplifying x + -13.5 = 13.586144903 Reorder the terms: -13.5 + x = 13.586144903 Solving -13.5 + x = 13.586144903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 13.586144903 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 13.586144903 + 13.5 x = 13.586144903 + 13.5 Combine like terms: 13.586144903 + 13.5 = 27.086144903 x = 27.086144903 Simplifying x = 27.086144903Subproblem 2
x + -13.5 = -13.586144903 Simplifying x + -13.5 = -13.586144903 Reorder the terms: -13.5 + x = -13.586144903 Solving -13.5 + x = -13.586144903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -13.586144903 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -13.586144903 + 13.5 x = -13.586144903 + 13.5 Combine like terms: -13.586144903 + 13.5 = -0.086144903 x = -0.086144903 Simplifying x = -0.086144903Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.086144903, -0.086144903}
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