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Simplifying 0 = -0.05x2 + 2.7x + 5.4 Reorder the terms: 0 = 5.4 + 2.7x + -0.05x2 Solving 0 = 5.4 + 2.7x + -0.05x2 Solving for variable 'x'. Combine like terms: 0 + -5.4 = -5.4 -5.4 + -2.7x + 0.05x2 = 5.4 + 2.7x + -0.05x2 + -5.4 + -2.7x + 0.05x2 Reorder the terms: -5.4 + -2.7x + 0.05x2 = 5.4 + -5.4 + 2.7x + -2.7x + -0.05x2 + 0.05x2 Combine like terms: 5.4 + -5.4 = 0.0 -5.4 + -2.7x + 0.05x2 = 0.0 + 2.7x + -2.7x + -0.05x2 + 0.05x2 -5.4 + -2.7x + 0.05x2 = 2.7x + -2.7x + -0.05x2 + 0.05x2 Combine like terms: 2.7x + -2.7x = 0.0 -5.4 + -2.7x + 0.05x2 = 0.0 + -0.05x2 + 0.05x2 -5.4 + -2.7x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 -5.4 + -2.7x + 0.05x2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -108 + -54x + x2 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + -54x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -54x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -54x + x2 = 0 + 108 -54x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -54x + x2 = 108 The x term is -54x. Take half its coefficient (-27). Square it (729) and add it to both sides. Add '729' to each side of the equation. -54x + 729 + x2 = 108 + 729 Reorder the terms: 729 + -54x + x2 = 108 + 729 Combine like terms: 108 + 729 = 837 729 + -54x + x2 = 837 Factor a perfect square on the left side: (x + -27)(x + -27) = 837 Calculate the square root of the right side: 28.930952283 Break this problem into two subproblems by setting (x + -27) equal to 28.930952283 and -28.930952283.Subproblem 1
x + -27 = 28.930952283 Simplifying x + -27 = 28.930952283 Reorder the terms: -27 + x = 28.930952283 Solving -27 + x = 28.930952283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = 28.930952283 + 27 Combine like terms: -27 + 27 = 0 0 + x = 28.930952283 + 27 x = 28.930952283 + 27 Combine like terms: 28.930952283 + 27 = 55.930952283 x = 55.930952283 Simplifying x = 55.930952283Subproblem 2
x + -27 = -28.930952283 Simplifying x + -27 = -28.930952283 Reorder the terms: -27 + x = -28.930952283 Solving -27 + x = -28.930952283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x = -28.930952283 + 27 Combine like terms: -27 + 27 = 0 0 + x = -28.930952283 + 27 x = -28.930952283 + 27 Combine like terms: -28.930952283 + 27 = -1.930952283 x = -1.930952283 Simplifying x = -1.930952283Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.930952283, -1.930952283}
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