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Simplifying 5400x2 + 2x + -30 = x Reorder the terms: -30 + 2x + 5400x2 = x Solving -30 + 2x + 5400x2 = x Solving for variable 'x'. Reorder the terms: -30 + 2x + -1x + 5400x2 = x + -1x Combine like terms: 2x + -1x = 1x -30 + 1x + 5400x2 = x + -1x Combine like terms: x + -1x = 0 -30 + 1x + 5400x2 = 0 Begin completing the square. Divide all terms by 5400 the coefficient of the squared term: Divide each side by '5400'. -0.005555555556 + 0.0001851851852x + x2 = 0 Move the constant term to the right: Add '0.005555555556' to each side of the equation. -0.005555555556 + 0.0001851851852x + 0.005555555556 + x2 = 0 + 0.005555555556 Reorder the terms: -0.005555555556 + 0.005555555556 + 0.0001851851852x + x2 = 0 + 0.005555555556 Combine like terms: -0.005555555556 + 0.005555555556 = 0.000000000000 0.000000000000 + 0.0001851851852x + x2 = 0 + 0.005555555556 0.0001851851852x + x2 = 0 + 0.005555555556 Combine like terms: 0 + 0.005555555556 = 0.005555555556 0.0001851851852x + x2 = 0.005555555556 The x term is 0.0001851851852x. Take half its coefficient (0.0000925925926). Square it (0.000000008573388204) and add it to both sides. Add '0.000000008573388204' to each side of the equation. 0.0001851851852x + 0.000000008573388204 + x2 = 0.005555555556 + 0.000000008573388204 Reorder the terms: 0.000000008573388204 + 0.0001851851852x + x2 = 0.005555555556 + 0.000000008573388204 Combine like terms: 0.005555555556 + 0.000000008573388204 = 0.005555564129388204 0.000000008573388204 + 0.0001851851852x + x2 = 0.005555564129388204 Factor a perfect square on the left side: (x + 0.0000925925926)(x + 0.0000925925926) = 0.005555564129388204 Calculate the square root of the right side: 0.074535657 Break this problem into two subproblems by setting (x + 0.0000925925926) equal to 0.074535657 and -0.074535657.Subproblem 1
x + 0.0000925925926 = 0.074535657 Simplifying x + 0.0000925925926 = 0.074535657 Reorder the terms: 0.0000925925926 + x = 0.074535657 Solving 0.0000925925926 + x = 0.074535657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000925925926' to each side of the equation. 0.0000925925926 + -0.0000925925926 + x = 0.074535657 + -0.0000925925926 Combine like terms: 0.0000925925926 + -0.0000925925926 = 0.0000000000000 0.0000000000000 + x = 0.074535657 + -0.0000925925926 x = 0.074535657 + -0.0000925925926 Combine like terms: 0.074535657 + -0.0000925925926 = 0.0744430644074 x = 0.0744430644074 Simplifying x = 0.0744430644074Subproblem 2
x + 0.0000925925926 = -0.074535657 Simplifying x + 0.0000925925926 = -0.074535657 Reorder the terms: 0.0000925925926 + x = -0.074535657 Solving 0.0000925925926 + x = -0.074535657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000925925926' to each side of the equation. 0.0000925925926 + -0.0000925925926 + x = -0.074535657 + -0.0000925925926 Combine like terms: 0.0000925925926 + -0.0000925925926 = 0.0000000000000 0.0000000000000 + x = -0.074535657 + -0.0000925925926 x = -0.074535657 + -0.0000925925926 Combine like terms: -0.074535657 + -0.0000925925926 = -0.0746282495926 x = -0.0746282495926 Simplifying x = -0.0746282495926Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0744430644074, -0.0746282495926}
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