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Simplifying 0.00000006192x4 + -0.1794x2 + 3.0996 = 0 Reorder the terms: 3.0996 + -0.1794x2 + 0.00000006192x4 = 0 Solving 3.0996 + -0.1794x2 + 0.00000006192x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.00000006192 the coefficient of the squared term: Divide each side by '0.00000006192'. 50058139.53 + -2897286.822x2 + x4 = 0 Move the constant term to the right: Add '-50058139.53' to each side of the equation. 50058139.53 + -2897286.822x2 + -50058139.53 + x4 = 0 + -50058139.53 Reorder the terms: 50058139.53 + -50058139.53 + -2897286.822x2 + x4 = 0 + -50058139.53 Combine like terms: 50058139.53 + -50058139.53 = 0.00 0.00 + -2897286.822x2 + x4 = 0 + -50058139.53 -2897286.822x2 + x4 = 0 + -50058139.53 Combine like terms: 0 + -50058139.53 = -50058139.53 -2897286.822x2 + x4 = -50058139.53 The x term is -2897286.822x2. Take half its coefficient (-1448643.411). Square it (2098567732000) and add it to both sides. Add '2098567732000' to each side of the equation. -2897286.822x2 + 2098567732000 + x4 = -50058139.53 + 2098567732000 Reorder the terms: 2098567732000 + -2897286.822x2 + x4 = -50058139.53 + 2098567732000 Combine like terms: -50058139.53 + 2098567732000 = 2098517673860.47 2098567732000 + -2897286.822x2 + x4 = 2098517673860.47 Factor a perfect square on the left side: (x2 + -1448643.411)(x2 + -1448643.411) = 2098517673860.47 Calculate the square root of the right side: 1448626.133224329 Break this problem into two subproblems by setting (x2 + -1448643.411) equal to 1448626.133224329 and -1448626.133224329.Subproblem 1
x2 + -1448643.411 = 1448626.133224329 Simplifying x2 + -1448643.411 = 1448626.133224329 Reorder the terms: -1448643.411 + x2 = 1448626.133224329 Solving -1448643.411 + x2 = 1448626.133224329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1448643.411' to each side of the equation. -1448643.411 + 1448643.411 + x2 = 1448626.133224329 + 1448643.411 Combine like terms: -1448643.411 + 1448643.411 = 0.000 0.000 + x2 = 1448626.133224329 + 1448643.411 x2 = 1448626.133224329 + 1448643.411 Combine like terms: 1448626.133224329 + 1448643.411 = 2897269.544224329 x2 = 2897269.544224329 Simplifying x2 = 2897269.544224329 Take the square root of each side: x = {-1702.136758379, 1702.136758379}Subproblem 2
x2 + -1448643.411 = -1448626.133224329 Simplifying x2 + -1448643.411 = -1448626.133224329 Reorder the terms: -1448643.411 + x2 = -1448626.133224329 Solving -1448643.411 + x2 = -1448626.133224329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1448643.411' to each side of the equation. -1448643.411 + 1448643.411 + x2 = -1448626.133224329 + 1448643.411 Combine like terms: -1448643.411 + 1448643.411 = 0.000 0.000 + x2 = -1448626.133224329 + 1448643.411 x2 = -1448626.133224329 + 1448643.411 Combine like terms: -1448626.133224329 + 1448643.411 = 17.277775671 x2 = 17.277775671 Simplifying x2 = 17.277775671 Take the square root of each side: x = {-4.156654384, 4.156654384}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1702.136758379, 1702.136758379, -4.156654384, 4.156654384}
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