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Simplifying 2x2 + 9x + -66 = 0 Reorder the terms: -66 + 9x + 2x2 = 0 Solving -66 + 9x + 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 + 4.5x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 4.5x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 4.5x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4.5x + x2 = 0 + 33 4.5x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 4.5x + x2 = 33 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 33 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 33 + 5.0625 Combine like terms: 33 + 5.0625 = 38.0625 5.0625 + 4.5x + x2 = 38.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 38.0625 Calculate the square root of the right side: 6.16948134 Break this problem into two subproblems by setting (x + 2.25) equal to 6.16948134 and -6.16948134.Subproblem 1
x + 2.25 = 6.16948134 Simplifying x + 2.25 = 6.16948134 Reorder the terms: 2.25 + x = 6.16948134 Solving 2.25 + x = 6.16948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 6.16948134 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 6.16948134 + -2.25 x = 6.16948134 + -2.25 Combine like terms: 6.16948134 + -2.25 = 3.91948134 x = 3.91948134 Simplifying x = 3.91948134Subproblem 2
x + 2.25 = -6.16948134 Simplifying x + 2.25 = -6.16948134 Reorder the terms: 2.25 + x = -6.16948134 Solving 2.25 + x = -6.16948134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -6.16948134 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -6.16948134 + -2.25 x = -6.16948134 + -2.25 Combine like terms: -6.16948134 + -2.25 = -8.41948134 x = -8.41948134 Simplifying x = -8.41948134Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.91948134, -8.41948134}
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