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Simplifying -2x2 + -11x + 60 = 0 Reorder the terms: 60 + -11x + -2x2 = 0 Solving 60 + -11x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -30 + 5.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 5.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 5.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 5.5x + x2 = 0 + 30 5.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 5.5x + x2 = 30 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 30 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 30 + 7.5625 Combine like terms: 30 + 7.5625 = 37.5625 7.5625 + 5.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + 2.75) equal to 6.128825336 and -6.128825336.Subproblem 1
x + 2.75 = 6.128825336 Simplifying x + 2.75 = 6.128825336 Reorder the terms: 2.75 + x = 6.128825336 Solving 2.75 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 6.128825336 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 6.128825336 + -2.75 x = 6.128825336 + -2.75 Combine like terms: 6.128825336 + -2.75 = 3.378825336 x = 3.378825336 Simplifying x = 3.378825336Subproblem 2
x + 2.75 = -6.128825336 Simplifying x + 2.75 = -6.128825336 Reorder the terms: 2.75 + x = -6.128825336 Solving 2.75 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -6.128825336 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -6.128825336 + -2.75 x = -6.128825336 + -2.75 Combine like terms: -6.128825336 + -2.75 = -8.878825336 x = -8.878825336 Simplifying x = -8.878825336Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.378825336, -8.878825336}
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