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Simplifying x4 + -200x2 + 100 = 0 Reorder the terms: 100 + -200x2 + x4 = 0 Solving 100 + -200x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -200x2 + -100 + x4 = 0 + -100 Reorder the terms: 100 + -100 + -200x2 + x4 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -200x2 + x4 = 0 + -100 -200x2 + x4 = 0 + -100 Combine like terms: 0 + -100 = -100 -200x2 + x4 = -100 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 = -100 + 10000 Reorder the terms: 10000 + -200x2 + x4 = -100 + 10000 Combine like terms: -100 + 10000 = 9900 10000 + -200x2 + x4 = 9900 Factor a perfect square on the left side: (x2 + -100)(x2 + -100) = 9900 Calculate the square root of the right side: 99.498743711 Break this problem into two subproblems by setting (x2 + -100) equal to 99.498743711 and -99.498743711.Subproblem 1
x2 + -100 = 99.498743711 Simplifying x2 + -100 = 99.498743711 Reorder the terms: -100 + x2 = 99.498743711 Solving -100 + x2 = 99.498743711 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 = 99.498743711 + 100 Combine like terms: -100 + 100 = 0 0 + x2 = 99.498743711 + 100 x2 = 99.498743711 + 100 Combine like terms: 99.498743711 + 100 = 199.498743711 x2 = 199.498743711 Simplifying x2 = 199.498743711 Take the square root of each side: x = {-14.12440242, 14.12440242}Subproblem 2
x2 + -100 = -99.498743711 Simplifying x2 + -100 = -99.498743711 Reorder the terms: -100 + x2 = -99.498743711 Solving -100 + x2 = -99.498743711 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 = -99.498743711 + 100 Combine like terms: -100 + 100 = 0 0 + x2 = -99.498743711 + 100 x2 = -99.498743711 + 100 Combine like terms: -99.498743711 + 100 = 0.501256289 x2 = 0.501256289 Simplifying x2 = 0.501256289 Take the square root of each side: x = {-0.707994554, 0.707994554}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-14.12440242, 14.12440242, -0.707994554, 0.707994554}
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