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Simplifying 6x2 + -66x + 181 = 0 Reorder the terms: 181 + -66x + 6x2 = 0 Solving 181 + -66x + 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'. 30.16666667 + -11x + x2 = 0 Move the constant term to the right: Add '-30.16666667' to each side of the equation. 30.16666667 + -11x + -30.16666667 + x2 = 0 + -30.16666667 Reorder the terms: 30.16666667 + -30.16666667 + -11x + x2 = 0 + -30.16666667 Combine like terms: 30.16666667 + -30.16666667 = 0.00000000 0.00000000 + -11x + x2 = 0 + -30.16666667 -11x + x2 = 0 + -30.16666667 Combine like terms: 0 + -30.16666667 = -30.16666667 -11x + x2 = -30.16666667 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -30.16666667 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -30.16666667 + 30.25 Combine like terms: -30.16666667 + 30.25 = 0.08333333 30.25 + -11x + x2 = 0.08333333 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 0.08333333 Calculate the square root of the right side: 0.288675129 Break this problem into two subproblems by setting (x + -5.5) equal to 0.288675129 and -0.288675129.Subproblem 1
x + -5.5 = 0.288675129 Simplifying x + -5.5 = 0.288675129 Reorder the terms: -5.5 + x = 0.288675129 Solving -5.5 + x = 0.288675129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 0.288675129 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 0.288675129 + 5.5 x = 0.288675129 + 5.5 Combine like terms: 0.288675129 + 5.5 = 5.788675129 x = 5.788675129 Simplifying x = 5.788675129Subproblem 2
x + -5.5 = -0.288675129 Simplifying x + -5.5 = -0.288675129 Reorder the terms: -5.5 + x = -0.288675129 Solving -5.5 + x = -0.288675129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -0.288675129 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -0.288675129 + 5.5 x = -0.288675129 + 5.5 Combine like terms: -0.288675129 + 5.5 = 5.211324871 x = 5.211324871 Simplifying x = 5.211324871Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.788675129, 5.211324871}
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