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Simplifying 2x2 + -33x + -60 = 0 Reorder the terms: -60 + -33x + 2x2 = 0 Solving -60 + -33x + 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 + -16.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -16.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -16.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -16.5x + x2 = 0 + 30 -16.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -16.5x + x2 = 30 The x term is -16.5x. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5x + 68.0625 + x2 = 30 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = 30 + 68.0625 Combine like terms: 30 + 68.0625 = 98.0625 68.0625 + -16.5x + x2 = 98.0625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 98.0625 Calculate the square root of the right side: 9.90265116 Break this problem into two subproblems by setting (x + -8.25) equal to 9.90265116 and -9.90265116.Subproblem 1
x + -8.25 = 9.90265116 Simplifying x + -8.25 = 9.90265116 Reorder the terms: -8.25 + x = 9.90265116 Solving -8.25 + x = 9.90265116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = 9.90265116 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 9.90265116 + 8.25 x = 9.90265116 + 8.25 Combine like terms: 9.90265116 + 8.25 = 18.15265116 x = 18.15265116 Simplifying x = 18.15265116Subproblem 2
x + -8.25 = -9.90265116 Simplifying x + -8.25 = -9.90265116 Reorder the terms: -8.25 + x = -9.90265116 Solving -8.25 + x = -9.90265116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = -9.90265116 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -9.90265116 + 8.25 x = -9.90265116 + 8.25 Combine like terms: -9.90265116 + 8.25 = -1.65265116 x = -1.65265116 Simplifying x = -1.65265116Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.15265116, -1.65265116}
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