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Simplifying 5x2 + 20x + -99 = 0 Reorder the terms: -99 + 20x + 5x2 = 0 Solving -99 + 20x + 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 + 4x + x2 = 0 Move the constant term to the right: Add '19.8' to each side of the equation. -19.8 + 4x + 19.8 + x2 = 0 + 19.8 Reorder the terms: -19.8 + 19.8 + 4x + x2 = 0 + 19.8 Combine like terms: -19.8 + 19.8 = 0.0 0.0 + 4x + x2 = 0 + 19.8 4x + x2 = 0 + 19.8 Combine like terms: 0 + 19.8 = 19.8 4x + x2 = 19.8 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 19.8 + 4 Reorder the terms: 4 + 4x + x2 = 19.8 + 4 Combine like terms: 19.8 + 4 = 23.8 4 + 4x + x2 = 23.8 Factor a perfect square on the left side: (x + 2)(x + 2) = 23.8 Calculate the square root of the right side: 4.878524367 Break this problem into two subproblems by setting (x + 2) equal to 4.878524367 and -4.878524367.Subproblem 1
x + 2 = 4.878524367 Simplifying x + 2 = 4.878524367 Reorder the terms: 2 + x = 4.878524367 Solving 2 + x = 4.878524367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.878524367 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.878524367 + -2 x = 4.878524367 + -2 Combine like terms: 4.878524367 + -2 = 2.878524367 x = 2.878524367 Simplifying x = 2.878524367Subproblem 2
x + 2 = -4.878524367 Simplifying x + 2 = -4.878524367 Reorder the terms: 2 + x = -4.878524367 Solving 2 + x = -4.878524367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.878524367 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.878524367 + -2 x = -4.878524367 + -2 Combine like terms: -4.878524367 + -2 = -6.878524367 x = -6.878524367 Simplifying x = -6.878524367Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.878524367, -6.878524367}
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