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Simplifying 3x2 + 33x + -80 = 0 Reorder the terms: -80 + 33x + 3x2 = 0 Solving -80 + 33x + 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'. -26.66666667 + 11x + x2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + 11x + 26.66666667 + x2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + 11x + x2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + 11x + x2 = 0 + 26.66666667 11x + x2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 11x + x2 = 26.66666667 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 = 26.66666667 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 26.66666667 + 30.25 Combine like terms: 26.66666667 + 30.25 = 56.91666667 30.25 + 11x + x2 = 56.91666667 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 56.91666667 Calculate the square root of the right side: 7.544313532 Break this problem into two subproblems by setting (x + 5.5) equal to 7.544313532 and -7.544313532.Subproblem 1
x + 5.5 = 7.544313532 Simplifying x + 5.5 = 7.544313532 Reorder the terms: 5.5 + x = 7.544313532 Solving 5.5 + x = 7.544313532 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 = 7.544313532 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.544313532 + -5.5 x = 7.544313532 + -5.5 Combine like terms: 7.544313532 + -5.5 = 2.044313532 x = 2.044313532 Simplifying x = 2.044313532Subproblem 2
x + 5.5 = -7.544313532 Simplifying x + 5.5 = -7.544313532 Reorder the terms: 5.5 + x = -7.544313532 Solving 5.5 + x = -7.544313532 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 = -7.544313532 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.544313532 + -5.5 x = -7.544313532 + -5.5 Combine like terms: -7.544313532 + -5.5 = -13.044313532 x = -13.044313532 Simplifying x = -13.044313532Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.044313532, -13.044313532}
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