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Simplifying 5x4 + -401x2 + 16 = 0 Reorder the terms: 16 + -401x2 + 5x4 = 0 Solving 16 + -401x2 + 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'. 3.2 + -80.2x2 + x4 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -80.2x2 + -3.2 + x4 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -80.2x2 + x4 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -80.2x2 + x4 = 0 + -3.2 -80.2x2 + x4 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -80.2x2 + x4 = -3.2 The x term is -80.2x2. Take half its coefficient (-40.1). Square it (1608.01) and add it to both sides. Add '1608.01' to each side of the equation. -80.2x2 + 1608.01 + x4 = -3.2 + 1608.01 Reorder the terms: 1608.01 + -80.2x2 + x4 = -3.2 + 1608.01 Combine like terms: -3.2 + 1608.01 = 1604.81 1608.01 + -80.2x2 + x4 = 1604.81 Factor a perfect square on the left side: (x2 + -40.1)(x2 + -40.1) = 1604.81 Calculate the square root of the right side: 40.06007988 Break this problem into two subproblems by setting (x2 + -40.1) equal to 40.06007988 and -40.06007988.Subproblem 1
x2 + -40.1 = 40.06007988 Simplifying x2 + -40.1 = 40.06007988 Reorder the terms: -40.1 + x2 = 40.06007988 Solving -40.1 + x2 = 40.06007988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.1' to each side of the equation. -40.1 + 40.1 + x2 = 40.06007988 + 40.1 Combine like terms: -40.1 + 40.1 = 0.0 0.0 + x2 = 40.06007988 + 40.1 x2 = 40.06007988 + 40.1 Combine like terms: 40.06007988 + 40.1 = 80.16007988 x2 = 80.16007988 Simplifying x2 = 80.16007988 Take the square root of each side: x = {-8.953216175, 8.953216175}Subproblem 2
x2 + -40.1 = -40.06007988 Simplifying x2 + -40.1 = -40.06007988 Reorder the terms: -40.1 + x2 = -40.06007988 Solving -40.1 + x2 = -40.06007988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.1' to each side of the equation. -40.1 + 40.1 + x2 = -40.06007988 + 40.1 Combine like terms: -40.1 + 40.1 = 0.0 0.0 + x2 = -40.06007988 + 40.1 x2 = -40.06007988 + 40.1 Combine like terms: -40.06007988 + 40.1 = 0.03992012 x2 = 0.03992012 Simplifying x2 = 0.03992012 Take the square root of each side: x = {-0.1998002, 0.1998002}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.953216175, 8.953216175, -0.1998002, 0.1998002}
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