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Simplifying x4 + -200x2 + 5000 = 0 Reorder the terms: 5000 + -200x2 + x4 = 0 Solving 5000 + -200x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -200x2 + -5000 + x4 = 0 + -5000 Reorder the terms: 5000 + -5000 + -200x2 + x4 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -200x2 + x4 = 0 + -5000 -200x2 + x4 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -200x2 + x4 = -5000 The x term is -200x2. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x2 + 10000 + x4 = -5000 + 10000 Reorder the terms: 10000 + -200x2 + x4 = -5000 + 10000 Combine like terms: -5000 + 10000 = 5000 10000 + -200x2 + x4 = 5000 Factor a perfect square on the left side: (x2 + -100)(x2 + -100) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (x2 + -100) equal to 70.710678119 and -70.710678119.Subproblem 1
x2 + -100 = 70.710678119 Simplifying x2 + -100 = 70.710678119 Reorder the terms: -100 + x2 = 70.710678119 Solving -100 + x2 = 70.710678119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x2 = 70.710678119 + 100 Combine like terms: -100 + 100 = 0 0 + x2 = 70.710678119 + 100 x2 = 70.710678119 + 100 Combine like terms: 70.710678119 + 100 = 170.710678119 x2 = 170.710678119 Simplifying x2 = 170.710678119 Take the square root of each side: x = {-13.065629649, 13.065629649}Subproblem 2
x2 + -100 = -70.710678119 Simplifying x2 + -100 = -70.710678119 Reorder the terms: -100 + x2 = -70.710678119 Solving -100 + x2 = -70.710678119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x2 = -70.710678119 + 100 Combine like terms: -100 + 100 = 0 0 + x2 = -70.710678119 + 100 x2 = -70.710678119 + 100 Combine like terms: -70.710678119 + 100 = 29.289321881 x2 = 29.289321881 Simplifying x2 = 29.289321881 Take the square root of each side: x = {-5.411961001, 5.411961001}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.065629649, 13.065629649, -5.411961001, 5.411961001}
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