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Simplifying x4 + -5x2 + 6.2 = 0 Reorder the terms: 6.2 + -5x2 + x4 = 0 Solving 6.2 + -5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6.2' to each side of the equation. 6.2 + -5x2 + -6.2 + x4 = 0 + -6.2 Reorder the terms: 6.2 + -6.2 + -5x2 + x4 = 0 + -6.2 Combine like terms: 6.2 + -6.2 = 0.0 0.0 + -5x2 + x4 = 0 + -6.2 -5x2 + x4 = 0 + -6.2 Combine like terms: 0 + -6.2 = -6.2 -5x2 + x4 = -6.2 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = -6.2 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = -6.2 + 6.25 Combine like terms: -6.2 + 6.25 = 0.05 6.25 + -5x2 + x4 = 0.05 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 0.05 Calculate the square root of the right side: 0.223606798 Break this problem into two subproblems by setting (x2 + -2.5) equal to 0.223606798 and -0.223606798.Subproblem 1
x2 + -2.5 = 0.223606798 Simplifying x2 + -2.5 = 0.223606798 Reorder the terms: -2.5 + x2 = 0.223606798 Solving -2.5 + x2 = 0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 0.223606798 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 0.223606798 + 2.5 x2 = 0.223606798 + 2.5 Combine like terms: 0.223606798 + 2.5 = 2.723606798 x2 = 2.723606798 Simplifying x2 = 2.723606798 Take the square root of each side: x = {-1.650335359, 1.650335359}Subproblem 2
x2 + -2.5 = -0.223606798 Simplifying x2 + -2.5 = -0.223606798 Reorder the terms: -2.5 + x2 = -0.223606798 Solving -2.5 + x2 = -0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -0.223606798 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -0.223606798 + 2.5 x2 = -0.223606798 + 2.5 Combine like terms: -0.223606798 + 2.5 = 2.276393202 x2 = 2.276393202 Simplifying x2 = 2.276393202 Take the square root of each side: x = {-1.508772084, 1.508772084}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.650335359, 1.650335359, -1.508772084, 1.508772084}
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