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Simplifying 5x4 + -8x2 + 1 = 0 Reorder the terms: 1 + -8x2 + 5x4 = 0 Solving 1 + -8x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -1.6x2 + x4 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.6x2 + -0.2 + x4 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.6x2 + x4 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.6x2 + x4 = 0 + -0.2 -1.6x2 + x4 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.6x2 + x4 = -0.2 The x term is -1.6x2. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x2 + 0.64 + x4 = -0.2 + 0.64 Reorder the terms: 0.64 + -1.6x2 + x4 = -0.2 + 0.64 Combine like terms: -0.2 + 0.64 = 0.44 0.64 + -1.6x2 + x4 = 0.44 Factor a perfect square on the left side: (x2 + -0.8)(x2 + -0.8) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x2 + -0.8) equal to 0.663324958 and -0.663324958.Subproblem 1
x2 + -0.8 = 0.663324958 Simplifying x2 + -0.8 = 0.663324958 Reorder the terms: -0.8 + x2 = 0.663324958 Solving -0.8 + x2 = 0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x2 = 0.663324958 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x2 = 0.663324958 + 0.8 x2 = 0.663324958 + 0.8 Combine like terms: 0.663324958 + 0.8 = 1.463324958 x2 = 1.463324958 Simplifying x2 = 1.463324958 Take the square root of each side: x = {-1.209679692, 1.209679692}Subproblem 2
x2 + -0.8 = -0.663324958 Simplifying x2 + -0.8 = -0.663324958 Reorder the terms: -0.8 + x2 = -0.663324958 Solving -0.8 + x2 = -0.663324958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x2 = -0.663324958 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x2 = -0.663324958 + 0.8 x2 = -0.663324958 + 0.8 Combine like terms: -0.663324958 + 0.8 = 0.136675042 x2 = 0.136675042 Simplifying x2 = 0.136675042 Take the square root of each side: x = {-0.369695878, 0.369695878}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.209679692, 1.209679692, -0.369695878, 0.369695878}
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