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Simplifying 2x2 + -9x + -99 = 0 Reorder the terms: -99 + -9x + 2x2 = 0 Solving -99 + -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'. -49.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '49.5' to each side of the equation. -49.5 + -4.5x + 49.5 + x2 = 0 + 49.5 Reorder the terms: -49.5 + 49.5 + -4.5x + x2 = 0 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + -4.5x + x2 = 0 + 49.5 -4.5x + x2 = 0 + 49.5 Combine like terms: 0 + 49.5 = 49.5 -4.5x + x2 = 49.5 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 = 49.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 49.5 + 5.0625 Combine like terms: 49.5 + 5.0625 = 54.5625 5.0625 + -4.5x + x2 = 54.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 54.5625 Calculate the square root of the right side: 7.386643351 Break this problem into two subproblems by setting (x + -2.25) equal to 7.386643351 and -7.386643351.Subproblem 1
x + -2.25 = 7.386643351 Simplifying x + -2.25 = 7.386643351 Reorder the terms: -2.25 + x = 7.386643351 Solving -2.25 + x = 7.386643351 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 = 7.386643351 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 7.386643351 + 2.25 x = 7.386643351 + 2.25 Combine like terms: 7.386643351 + 2.25 = 9.636643351 x = 9.636643351 Simplifying x = 9.636643351Subproblem 2
x + -2.25 = -7.386643351 Simplifying x + -2.25 = -7.386643351 Reorder the terms: -2.25 + x = -7.386643351 Solving -2.25 + x = -7.386643351 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 = -7.386643351 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -7.386643351 + 2.25 x = -7.386643351 + 2.25 Combine like terms: -7.386643351 + 2.25 = -5.136643351 x = -5.136643351 Simplifying x = -5.136643351Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.636643351, -5.136643351}
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