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Simplifying -2.7x2 + 27x + 6 = 0 Reorder the terms: 6 + 27x + -2.7x2 = 0 Solving 6 + 27x + -2.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. -2.222222222 + -10x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -10x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -10x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -10x + x2 = 0 + 2.222222222 -10x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -10x + x2 = 2.222222222 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 2.222222222 + 25 Reorder the terms: 25 + -10x + x2 = 2.222222222 + 25 Combine like terms: 2.222222222 + 25 = 27.222222222 25 + -10x + x2 = 27.222222222 Factor a perfect square on the left side: (x + -5)(x + -5) = 27.222222222 Calculate the square root of the right side: 5.217491947 Break this problem into two subproblems by setting (x + -5) equal to 5.217491947 and -5.217491947.Subproblem 1
x + -5 = 5.217491947 Simplifying x + -5 = 5.217491947 Reorder the terms: -5 + x = 5.217491947 Solving -5 + x = 5.217491947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.217491947 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.217491947 + 5 x = 5.217491947 + 5 Combine like terms: 5.217491947 + 5 = 10.217491947 x = 10.217491947 Simplifying x = 10.217491947Subproblem 2
x + -5 = -5.217491947 Simplifying x + -5 = -5.217491947 Reorder the terms: -5 + x = -5.217491947 Solving -5 + x = -5.217491947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.217491947 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.217491947 + 5 x = -5.217491947 + 5 Combine like terms: -5.217491947 + 5 = -0.217491947 x = -0.217491947 Simplifying x = -0.217491947Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.217491947, -0.217491947}
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