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Simplifying 27x2 + 54x + 2 = 0 Reorder the terms: 2 + 54x + 27x2 = 0 Solving 2 + 54x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.07407407407 + 2x + x2 = 0 Move the constant term to the right: Add '-0.07407407407' to each side of the equation. 0.07407407407 + 2x + -0.07407407407 + x2 = 0 + -0.07407407407 Reorder the terms: 0.07407407407 + -0.07407407407 + 2x + x2 = 0 + -0.07407407407 Combine like terms: 0.07407407407 + -0.07407407407 = 0.00000000000 0.00000000000 + 2x + x2 = 0 + -0.07407407407 2x + x2 = 0 + -0.07407407407 Combine like terms: 0 + -0.07407407407 = -0.07407407407 2x + x2 = -0.07407407407 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.07407407407 + 1 Reorder the terms: 1 + 2x + x2 = -0.07407407407 + 1 Combine like terms: -0.07407407407 + 1 = 0.92592592593 1 + 2x + x2 = 0.92592592593 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.92592592593 Calculate the square root of the right side: 0.962250449 Break this problem into two subproblems by setting (x + 1) equal to 0.962250449 and -0.962250449.Subproblem 1
x + 1 = 0.962250449 Simplifying x + 1 = 0.962250449 Reorder the terms: 1 + x = 0.962250449 Solving 1 + x = 0.962250449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.962250449 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.962250449 + -1 x = 0.962250449 + -1 Combine like terms: 0.962250449 + -1 = -0.037749551 x = -0.037749551 Simplifying x = -0.037749551Subproblem 2
x + 1 = -0.962250449 Simplifying x + 1 = -0.962250449 Reorder the terms: 1 + x = -0.962250449 Solving 1 + x = -0.962250449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.962250449 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.962250449 + -1 x = -0.962250449 + -1 Combine like terms: -0.962250449 + -1 = -1.962250449 x = -1.962250449 Simplifying x = -1.962250449Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.037749551, -1.962250449}
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