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Simplifying 27x2 + 12x + -2 = 0 Reorder the terms: -2 + 12x + 27x2 = 0 Solving -2 + 12x + 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 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.07407407407' to each side of the equation. -0.07407407407 + 0.4444444444x + 0.07407407407 + x2 = 0 + 0.07407407407 Reorder the terms: -0.07407407407 + 0.07407407407 + 0.4444444444x + x2 = 0 + 0.07407407407 Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000 0.00000000000 + 0.4444444444x + x2 = 0 + 0.07407407407 0.4444444444x + x2 = 0 + 0.07407407407 Combine like terms: 0 + 0.07407407407 = 0.07407407407 0.4444444444x + x2 = 0.07407407407 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 0.07407407407 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 0.07407407407 + 0.04938271604 Combine like terms: 0.07407407407 + 0.04938271604 = 0.12345679011 0.04938271604 + 0.4444444444x + x2 = 0.12345679011 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 0.12345679011 Calculate the square root of the right side: 0.351364184 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 0.351364184 and -0.351364184.Subproblem 1
x + 0.2222222222 = 0.351364184 Simplifying x + 0.2222222222 = 0.351364184 Reorder the terms: 0.2222222222 + x = 0.351364184 Solving 0.2222222222 + x = 0.351364184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 0.351364184 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 0.351364184 + -0.2222222222 x = 0.351364184 + -0.2222222222 Combine like terms: 0.351364184 + -0.2222222222 = 0.1291419618 x = 0.1291419618 Simplifying x = 0.1291419618Subproblem 2
x + 0.2222222222 = -0.351364184 Simplifying x + 0.2222222222 = -0.351364184 Reorder the terms: 0.2222222222 + x = -0.351364184 Solving 0.2222222222 + x = -0.351364184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -0.351364184 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -0.351364184 + -0.2222222222 x = -0.351364184 + -0.2222222222 Combine like terms: -0.351364184 + -0.2222222222 = -0.5735864062 x = -0.5735864062 Simplifying x = -0.5735864062Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1291419618, -0.5735864062}
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