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Simplifying 27x2 + -14x = 3 Reorder the terms: -14x + 27x2 = 3 Solving -14x + 27x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -14x + 27x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -14x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.1111111111 + -0.5185185185x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.5185185185x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.5185185185x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.5185185185x + x2 = 0 + 0.1111111111 -0.5185185185x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.5185185185x + x2 = 0.1111111111 The x term is -0.5185185185x. Take half its coefficient (-0.2592592593). Square it (0.06721536353) and add it to both sides. Add '0.06721536353' to each side of the equation. -0.5185185185x + 0.06721536353 + x2 = 0.1111111111 + 0.06721536353 Reorder the terms: 0.06721536353 + -0.5185185185x + x2 = 0.1111111111 + 0.06721536353 Combine like terms: 0.1111111111 + 0.06721536353 = 0.17832647463 0.06721536353 + -0.5185185185x + x2 = 0.17832647463 Factor a perfect square on the left side: (x + -0.2592592593)(x + -0.2592592593) = 0.17832647463 Calculate the square root of the right side: 0.422287194 Break this problem into two subproblems by setting (x + -0.2592592593) equal to 0.422287194 and -0.422287194.Subproblem 1
x + -0.2592592593 = 0.422287194 Simplifying x + -0.2592592593 = 0.422287194 Reorder the terms: -0.2592592593 + x = 0.422287194 Solving -0.2592592593 + x = 0.422287194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2592592593' to each side of the equation. -0.2592592593 + 0.2592592593 + x = 0.422287194 + 0.2592592593 Combine like terms: -0.2592592593 + 0.2592592593 = 0.0000000000 0.0000000000 + x = 0.422287194 + 0.2592592593 x = 0.422287194 + 0.2592592593 Combine like terms: 0.422287194 + 0.2592592593 = 0.6815464533 x = 0.6815464533 Simplifying x = 0.6815464533Subproblem 2
x + -0.2592592593 = -0.422287194 Simplifying x + -0.2592592593 = -0.422287194 Reorder the terms: -0.2592592593 + x = -0.422287194 Solving -0.2592592593 + x = -0.422287194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2592592593' to each side of the equation. -0.2592592593 + 0.2592592593 + x = -0.422287194 + 0.2592592593 Combine like terms: -0.2592592593 + 0.2592592593 = 0.0000000000 0.0000000000 + x = -0.422287194 + 0.2592592593 x = -0.422287194 + 0.2592592593 Combine like terms: -0.422287194 + 0.2592592593 = -0.1630279347 x = -0.1630279347 Simplifying x = -0.1630279347Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6815464533, -0.1630279347}
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