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Simplifying 0.2x4 + -2x2 + 1.8 = 0 Reorder the terms: 1.8 + -2x2 + 0.2x4 = 0 Solving 1.8 + -2x2 + 0.2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 9 + -10x2 + x4 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -10x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -10x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -10x2 + x4 = 0 + -9 -10x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -10x2 + x4 = -9 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 = -9 + 25 Reorder the terms: 25 + -10x2 + x4 = -9 + 25 Combine like terms: -9 + 25 = 16 25 + -10x2 + x4 = 16 Factor a perfect square on the left side: (x2 + -5)(x2 + -5) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x2 + -5) equal to 4 and -4.Subproblem 1
x2 + -5 = 4 Simplifying x2 + -5 = 4 Reorder the terms: -5 + x2 = 4 Solving -5 + x2 = 4 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 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 4 + 5 x2 = 4 + 5 Combine like terms: 4 + 5 = 9 x2 = 9 Simplifying x2 = 9 Take the square root of each side: x = {-3, 3}Subproblem 2
x2 + -5 = -4 Simplifying x2 + -5 = -4 Reorder the terms: -5 + x2 = -4 Solving -5 + x2 = -4 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 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -4 + 5 x2 = -4 + 5 Combine like terms: -4 + 5 = 1 x2 = 1 Simplifying x2 = 1 Take the square root of each side: x = {-1, 1}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3, 3, -1, 1}
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