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Simplifying x4 + -0.56x2 + 0.0574 = 0 Reorder the terms: 0.0574 + -0.56x2 + x4 = 0 Solving 0.0574 + -0.56x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0574' to each side of the equation. 0.0574 + -0.56x2 + -0.0574 + x4 = 0 + -0.0574 Reorder the terms: 0.0574 + -0.0574 + -0.56x2 + x4 = 0 + -0.0574 Combine like terms: 0.0574 + -0.0574 = 0.0000 0.0000 + -0.56x2 + x4 = 0 + -0.0574 -0.56x2 + x4 = 0 + -0.0574 Combine like terms: 0 + -0.0574 = -0.0574 -0.56x2 + x4 = -0.0574 The x term is -0.56x2. Take half its coefficient (-0.28). Square it (0.0784) and add it to both sides. Add '0.0784' to each side of the equation. -0.56x2 + 0.0784 + x4 = -0.0574 + 0.0784 Reorder the terms: 0.0784 + -0.56x2 + x4 = -0.0574 + 0.0784 Combine like terms: -0.0574 + 0.0784 = 0.021 0.0784 + -0.56x2 + x4 = 0.021 Factor a perfect square on the left side: (x2 + -0.28)(x2 + -0.28) = 0.021 Calculate the square root of the right side: 0.144913767 Break this problem into two subproblems by setting (x2 + -0.28) equal to 0.144913767 and -0.144913767.Subproblem 1
x2 + -0.28 = 0.144913767 Simplifying x2 + -0.28 = 0.144913767 Reorder the terms: -0.28 + x2 = 0.144913767 Solving -0.28 + x2 = 0.144913767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28' to each side of the equation. -0.28 + 0.28 + x2 = 0.144913767 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + x2 = 0.144913767 + 0.28 x2 = 0.144913767 + 0.28 Combine like terms: 0.144913767 + 0.28 = 0.424913767 x2 = 0.424913767 Simplifying x2 = 0.424913767 Take the square root of each side: x = {-0.651854099, 0.651854099}Subproblem 2
x2 + -0.28 = -0.144913767 Simplifying x2 + -0.28 = -0.144913767 Reorder the terms: -0.28 + x2 = -0.144913767 Solving -0.28 + x2 = -0.144913767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28' to each side of the equation. -0.28 + 0.28 + x2 = -0.144913767 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + x2 = -0.144913767 + 0.28 x2 = -0.144913767 + 0.28 Combine like terms: -0.144913767 + 0.28 = 0.135086233 x2 = 0.135086233 Simplifying x2 = 0.135086233 Take the square root of each side: x = {-0.367540791, 0.367540791}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.651854099, 0.651854099, -0.367540791, 0.367540791}
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