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Simplifying (0.0000006192x4) + -1(0.1794x2) + 3.0996 = 0 Remove parenthesis around (0.1794x2) (0.0000006192x4) + -1 * 0.1794x2 + 3.0996 = 0 Multiply -1 * 0.1794 (0.0000006192x4) + -0.1794x2 + 3.0996 = 0 Reorder the terms: 3.0996 + -0.1794x2 + (0.0000006192x4) = 0 Solving 3.0996 + -0.1794x2 + (0.0000006192x4) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0000006192 the coefficient of the squared term: Divide each side by '0.0000006192'. 5005813.953 + -289728.6822x2 + x4 = 0 Move the constant term to the right: Add '-5005813.953' to each side of the equation. 5005813.953 + -289728.6822x2 + -5005813.953 + x4 = 0 + -5005813.953 Reorder the terms: 5005813.953 + -5005813.953 + -289728.6822x2 + x4 = 0 + -5005813.953 Combine like terms: 5005813.953 + -5005813.953 = 0.000 0.000 + -289728.6822x2 + x4 = 0 + -5005813.953 -289728.6822x2 + x4 = 0 + -5005813.953 Combine like terms: 0 + -5005813.953 = -5005813.953 -289728.6822x2 + x4 = -5005813.953 The x term is -289728.6822x2. Take half its coefficient (-144864.3411). Square it (20985677320) and add it to both sides. Add '20985677320' to each side of the equation. -289728.6822x2 + 20985677320 + x4 = -5005813.953 + 20985677320 Reorder the terms: 20985677320 + -289728.6822x2 + x4 = -5005813.953 + 20985677320 Combine like terms: -5005813.953 + 20985677320 = 20980671506.047 20985677320 + -289728.6822x2 + x4 = 20980671506.047 Factor a perfect square on the left side: ((x2) + -144864.3411)((x2) + -144864.3411) = 20980671506.047 Calculate the square root of the right side: 144847.062469513 Break this problem into two subproblems by setting ((x2) + -144864.3411) equal to 144847.062469513 and -144847.062469513.Subproblem 1
(x2) + -144864.3411 = 144847.062469513 Simplifying (x2) + -144864.3411 = 144847.062469513 x2 + -144864.3411 = 144847.062469513 Reorder the terms: -144864.3411 + x2 = 144847.062469513 Solving -144864.3411 + x2 = 144847.062469513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '144864.3411' to each side of the equation. -144864.3411 + 144864.3411 + x2 = 144847.062469513 + 144864.3411 Combine like terms: -144864.3411 + 144864.3411 = 0.0000 0.0000 + x2 = 144847.062469513 + 144864.3411 x2 = 144847.062469513 + 144864.3411 Combine like terms: 144847.062469513 + 144864.3411 = 289711.403569513 x2 = 289711.403569513 Simplifying x2 = 289711.403569513 Take the square root of each side: x = {-538.248458957, 538.248458957}Subproblem 2
(x2) + -144864.3411 = -144847.062469513 Simplifying (x2) + -144864.3411 = -144847.062469513 x2 + -144864.3411 = -144847.062469513 Reorder the terms: -144864.3411 + x2 = -144847.062469513 Solving -144864.3411 + x2 = -144847.062469513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '144864.3411' to each side of the equation. -144864.3411 + 144864.3411 + x2 = -144847.062469513 + 144864.3411 Combine like terms: -144864.3411 + 144864.3411 = 0.0000 0.0000 + x2 = -144847.062469513 + 144864.3411 x2 = -144847.062469513 + 144864.3411 Combine like terms: -144847.062469513 + 144864.3411 = 17.278630487 x2 = 17.278630487 Simplifying x2 = 17.278630487 Take the square root of each side: x = {-4.156757208, 4.156757208}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-538.248458957, 538.248458957, -4.156757208, 4.156757208}
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