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Simplifying 2x2 + -36x + 33 = 0 Reorder the terms: 33 + -36x + 2x2 = 0 Solving 33 + -36x + 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'. 16.5 + -18x + x2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + -18x + -16.5 + x2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + -18x + x2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + -18x + x2 = 0 + -16.5 -18x + x2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 -18x + x2 = -16.5 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -16.5 + 81 Reorder the terms: 81 + -18x + x2 = -16.5 + 81 Combine like terms: -16.5 + 81 = 64.5 81 + -18x + x2 = 64.5 Factor a perfect square on the left side: (x + -9)(x + -9) = 64.5 Calculate the square root of the right side: 8.031189202 Break this problem into two subproblems by setting (x + -9) equal to 8.031189202 and -8.031189202.Subproblem 1
x + -9 = 8.031189202 Simplifying x + -9 = 8.031189202 Reorder the terms: -9 + x = 8.031189202 Solving -9 + x = 8.031189202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 8.031189202 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.031189202 + 9 x = 8.031189202 + 9 Combine like terms: 8.031189202 + 9 = 17.031189202 x = 17.031189202 Simplifying x = 17.031189202Subproblem 2
x + -9 = -8.031189202 Simplifying x + -9 = -8.031189202 Reorder the terms: -9 + x = -8.031189202 Solving -9 + x = -8.031189202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -8.031189202 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.031189202 + 9 x = -8.031189202 + 9 Combine like terms: -8.031189202 + 9 = 0.968810798 x = 0.968810798 Simplifying x = 0.968810798Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.031189202, 0.968810798}
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