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Simplifying x4 + -38.94x2 + 0.00392 = 0 Reorder the terms: 0.00392 + -38.94x2 + x4 = 0 Solving 0.00392 + -38.94x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.00392' to each side of the equation. 0.00392 + -38.94x2 + -0.00392 + x4 = 0 + -0.00392 Reorder the terms: 0.00392 + -0.00392 + -38.94x2 + x4 = 0 + -0.00392 Combine like terms: 0.00392 + -0.00392 = 0.00000 0.00000 + -38.94x2 + x4 = 0 + -0.00392 -38.94x2 + x4 = 0 + -0.00392 Combine like terms: 0 + -0.00392 = -0.00392 -38.94x2 + x4 = -0.00392 The x term is -38.94x2. Take half its coefficient (-19.47). Square it (379.0809) and add it to both sides. Add '379.0809' to each side of the equation. -38.94x2 + 379.0809 + x4 = -0.00392 + 379.0809 Reorder the terms: 379.0809 + -38.94x2 + x4 = -0.00392 + 379.0809 Combine like terms: -0.00392 + 379.0809 = 379.07698 379.0809 + -38.94x2 + x4 = 379.07698 Factor a perfect square on the left side: (x2 + -19.47)(x2 + -19.47) = 379.07698 Calculate the square root of the right side: 19.469899332 Break this problem into two subproblems by setting (x2 + -19.47) equal to 19.469899332 and -19.469899332.Subproblem 1
x2 + -19.47 = 19.469899332 Simplifying x2 + -19.47 = 19.469899332 Reorder the terms: -19.47 + x2 = 19.469899332 Solving -19.47 + x2 = 19.469899332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.47' to each side of the equation. -19.47 + 19.47 + x2 = 19.469899332 + 19.47 Combine like terms: -19.47 + 19.47 = 0.00 0.00 + x2 = 19.469899332 + 19.47 x2 = 19.469899332 + 19.47 Combine like terms: 19.469899332 + 19.47 = 38.939899332 x2 = 38.939899332 Simplifying x2 = 38.939899332 Take the square root of each side: x = {-6.240184239, 6.240184239}Subproblem 2
x2 + -19.47 = -19.469899332 Simplifying x2 + -19.47 = -19.469899332 Reorder the terms: -19.47 + x2 = -19.469899332 Solving -19.47 + x2 = -19.469899332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.47' to each side of the equation. -19.47 + 19.47 + x2 = -19.469899332 + 19.47 Combine like terms: -19.47 + 19.47 = 0.00 0.00 + x2 = -19.469899332 + 19.47 x2 = -19.469899332 + 19.47 Combine like terms: -19.469899332 + 19.47 = 0.000100668 x2 = 0.000100668 Simplifying x2 = 0.000100668 Take the square root of each side: x = {-0.010033344, 0.010033344}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.240184239, 6.240184239, -0.010033344, 0.010033344}
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