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Simplifying 5x2 + 30x + -99 = 0 Reorder the terms: -99 + 30x + 5x2 = 0 Solving -99 + 30x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.8 + 6x + x2 = 0 Move the constant term to the right: Add '19.8' to each side of the equation. -19.8 + 6x + 19.8 + x2 = 0 + 19.8 Reorder the terms: -19.8 + 19.8 + 6x + x2 = 0 + 19.8 Combine like terms: -19.8 + 19.8 = 0.0 0.0 + 6x + x2 = 0 + 19.8 6x + x2 = 0 + 19.8 Combine like terms: 0 + 19.8 = 19.8 6x + x2 = 19.8 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 19.8 + 9 Reorder the terms: 9 + 6x + x2 = 19.8 + 9 Combine like terms: 19.8 + 9 = 28.8 9 + 6x + x2 = 28.8 Factor a perfect square on the left side: (x + 3)(x + 3) = 28.8 Calculate the square root of the right side: 5.366563146 Break this problem into two subproblems by setting (x + 3) equal to 5.366563146 and -5.366563146.Subproblem 1
x + 3 = 5.366563146 Simplifying x + 3 = 5.366563146 Reorder the terms: 3 + x = 5.366563146 Solving 3 + x = 5.366563146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.366563146 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.366563146 + -3 x = 5.366563146 + -3 Combine like terms: 5.366563146 + -3 = 2.366563146 x = 2.366563146 Simplifying x = 2.366563146Subproblem 2
x + 3 = -5.366563146 Simplifying x + 3 = -5.366563146 Reorder the terms: 3 + x = -5.366563146 Solving 3 + x = -5.366563146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.366563146 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.366563146 + -3 x = -5.366563146 + -3 Combine like terms: -5.366563146 + -3 = -8.366563146 x = -8.366563146 Simplifying x = -8.366563146Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.366563146, -8.366563146}
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