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Simplifying 2x2 + -27x = -16 Reorder the terms: -27x + 2x2 = -16 Solving -27x + 2x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + -27x + 2x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -27x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8 + -13.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -13.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -13.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -13.5x + x2 = 0 + -8 -13.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -13.5x + x2 = -8 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -8 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -8 + 45.5625 Combine like terms: -8 + 45.5625 = 37.5625 45.5625 + -13.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + -6.75) equal to 6.128825336 and -6.128825336.Subproblem 1
x + -6.75 = 6.128825336 Simplifying x + -6.75 = 6.128825336 Reorder the terms: -6.75 + x = 6.128825336 Solving -6.75 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 6.128825336 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 6.128825336 + 6.75 x = 6.128825336 + 6.75 Combine like terms: 6.128825336 + 6.75 = 12.878825336 x = 12.878825336 Simplifying x = 12.878825336Subproblem 2
x + -6.75 = -6.128825336 Simplifying x + -6.75 = -6.128825336 Reorder the terms: -6.75 + x = -6.128825336 Solving -6.75 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -6.128825336 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -6.128825336 + 6.75 x = -6.128825336 + 6.75 Combine like terms: -6.128825336 + 6.75 = 0.621174664 x = 0.621174664 Simplifying x = 0.621174664Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.878825336, 0.621174664}
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