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Simplifying -1x2 + 0.1x4 + 0.4 = 0 Reorder the terms: 0.4 + -1x2 + 0.1x4 = 0 Solving 0.4 + -1x2 + 0.1x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 4 + -10x2 + x4 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -10x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10x2 + x4 = 0 + -4 -10x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -10x2 + x4 = -4 The x term is -10x2. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x2 + 25 + x4 = -4 + 25 Reorder the terms: 25 + -10x2 + x4 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + -10x2 + x4 = 21 Factor a perfect square on the left side: (x2 + -5)(x2 + -5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x2 + -5) equal to 4.582575695 and -4.582575695.Subproblem 1
x2 + -5 = 4.582575695 Simplifying x2 + -5 = 4.582575695 Reorder the terms: -5 + x2 = 4.582575695 Solving -5 + x2 = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = 4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 4.582575695 + 5 x2 = 4.582575695 + 5 Combine like terms: 4.582575695 + 5 = 9.582575695 x2 = 9.582575695 Simplifying x2 = 9.582575695 Take the square root of each side: x = {-3.095573565, 3.095573565}Subproblem 2
x2 + -5 = -4.582575695 Simplifying x2 + -5 = -4.582575695 Reorder the terms: -5 + x2 = -4.582575695 Solving -5 + x2 = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = -4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -4.582575695 + 5 x2 = -4.582575695 + 5 Combine like terms: -4.582575695 + 5 = 0.417424305 x2 = 0.417424305 Simplifying x2 = 0.417424305 Take the square root of each side: x = {-0.646083822, 0.646083822}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.095573565, 3.095573565, -0.646083822, 0.646083822}
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