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Simplifying 2x2 + 23x + -5.7 = 0 Reorder the terms: -5.7 + 23x + 2x2 = 0 Solving -5.7 + 23x + 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'. -2.85 + 11.5x + x2 = 0 Move the constant term to the right: Add '2.85' to each side of the equation. -2.85 + 11.5x + 2.85 + x2 = 0 + 2.85 Reorder the terms: -2.85 + 2.85 + 11.5x + x2 = 0 + 2.85 Combine like terms: -2.85 + 2.85 = 0.00 0.00 + 11.5x + x2 = 0 + 2.85 11.5x + x2 = 0 + 2.85 Combine like terms: 0 + 2.85 = 2.85 11.5x + x2 = 2.85 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = 2.85 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = 2.85 + 33.0625 Combine like terms: 2.85 + 33.0625 = 35.9125 33.0625 + 11.5x + x2 = 35.9125 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 35.9125 Calculate the square root of the right side: 5.992703897 Break this problem into two subproblems by setting (x + 5.75) equal to 5.992703897 and -5.992703897.Subproblem 1
x + 5.75 = 5.992703897 Simplifying x + 5.75 = 5.992703897 Reorder the terms: 5.75 + x = 5.992703897 Solving 5.75 + x = 5.992703897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 5.992703897 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 5.992703897 + -5.75 x = 5.992703897 + -5.75 Combine like terms: 5.992703897 + -5.75 = 0.242703897 x = 0.242703897 Simplifying x = 0.242703897Subproblem 2
x + 5.75 = -5.992703897 Simplifying x + 5.75 = -5.992703897 Reorder the terms: 5.75 + x = -5.992703897 Solving 5.75 + x = -5.992703897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -5.992703897 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -5.992703897 + -5.75 x = -5.992703897 + -5.75 Combine like terms: -5.992703897 + -5.75 = -11.742703897 x = -11.742703897 Simplifying x = -11.742703897Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.242703897, -11.742703897}
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