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Simplifying 6x2 + -18x + -77 = 0 Reorder the terms: -77 + -18x + 6x2 = 0 Solving -77 + -18x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -12.83333333 + -3x + x2 = 0 Move the constant term to the right: Add '12.83333333' to each side of the equation. -12.83333333 + -3x + 12.83333333 + x2 = 0 + 12.83333333 Reorder the terms: -12.83333333 + 12.83333333 + -3x + x2 = 0 + 12.83333333 Combine like terms: -12.83333333 + 12.83333333 = 0.00000000 0.00000000 + -3x + x2 = 0 + 12.83333333 -3x + x2 = 0 + 12.83333333 Combine like terms: 0 + 12.83333333 = 12.83333333 -3x + x2 = 12.83333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 12.83333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 12.83333333 + 2.25 Combine like terms: 12.83333333 + 2.25 = 15.08333333 2.25 + -3x + x2 = 15.08333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 15.08333333 Calculate the square root of the right side: 3.883726732 Break this problem into two subproblems by setting (x + -1.5) equal to 3.883726732 and -3.883726732.Subproblem 1
x + -1.5 = 3.883726732 Simplifying x + -1.5 = 3.883726732 Reorder the terms: -1.5 + x = 3.883726732 Solving -1.5 + x = 3.883726732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.883726732 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.883726732 + 1.5 x = 3.883726732 + 1.5 Combine like terms: 3.883726732 + 1.5 = 5.383726732 x = 5.383726732 Simplifying x = 5.383726732Subproblem 2
x + -1.5 = -3.883726732 Simplifying x + -1.5 = -3.883726732 Reorder the terms: -1.5 + x = -3.883726732 Solving -1.5 + x = -3.883726732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.883726732 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.883726732 + 1.5 x = -3.883726732 + 1.5 Combine like terms: -3.883726732 + 1.5 = -2.383726732 x = -2.383726732 Simplifying x = -2.383726732Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.383726732, -2.383726732}
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