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Simplifying 2x2 + -17x + -66 = 0 Reorder the terms: -66 + -17x + 2x2 = 0 Solving -66 + -17x + 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'. -33 + -8.5x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + -8.5x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -8.5x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -8.5x + x2 = 0 + 33 -8.5x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -8.5x + x2 = 33 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 33 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 33 + 18.0625 Combine like terms: 33 + 18.0625 = 51.0625 18.0625 + -8.5x + x2 = 51.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 51.0625 Calculate the square root of the right side: 7.145802964 Break this problem into two subproblems by setting (x + -4.25) equal to 7.145802964 and -7.145802964.Subproblem 1
x + -4.25 = 7.145802964 Simplifying x + -4.25 = 7.145802964 Reorder the terms: -4.25 + x = 7.145802964 Solving -4.25 + x = 7.145802964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 7.145802964 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 7.145802964 + 4.25 x = 7.145802964 + 4.25 Combine like terms: 7.145802964 + 4.25 = 11.395802964 x = 11.395802964 Simplifying x = 11.395802964Subproblem 2
x + -4.25 = -7.145802964 Simplifying x + -4.25 = -7.145802964 Reorder the terms: -4.25 + x = -7.145802964 Solving -4.25 + x = -7.145802964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -7.145802964 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -7.145802964 + 4.25 x = -7.145802964 + 4.25 Combine like terms: -7.145802964 + 4.25 = -2.895802964 x = -2.895802964 Simplifying x = -2.895802964Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.395802964, -2.895802964}
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