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Simplifying x4 + -20x2 + 10 = 0 Reorder the terms: 10 + -20x2 + x4 = 0 Solving 10 + -20x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -20x2 + -10 + x4 = 0 + -10 Reorder the terms: 10 + -10 + -20x2 + x4 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -20x2 + x4 = 0 + -10 -20x2 + x4 = 0 + -10 Combine like terms: 0 + -10 = -10 -20x2 + x4 = -10 The x term is -20x2. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x2 + 100 + x4 = -10 + 100 Reorder the terms: 100 + -20x2 + x4 = -10 + 100 Combine like terms: -10 + 100 = 90 100 + -20x2 + x4 = 90 Factor a perfect square on the left side: (x2 + -10)(x2 + -10) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x2 + -10) equal to 9.486832981 and -9.486832981.Subproblem 1
x2 + -10 = 9.486832981 Simplifying x2 + -10 = 9.486832981 Reorder the terms: -10 + x2 = 9.486832981 Solving -10 + x2 = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = 9.486832981 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = 9.486832981 + 10 x2 = 9.486832981 + 10 Combine like terms: 9.486832981 + 10 = 19.486832981 x2 = 19.486832981 Simplifying x2 = 19.486832981 Take the square root of each side: x = {-4.41438931, 4.41438931}Subproblem 2
x2 + -10 = -9.486832981 Simplifying x2 + -10 = -9.486832981 Reorder the terms: -10 + x2 = -9.486832981 Solving -10 + x2 = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = -9.486832981 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = -9.486832981 + 10 x2 = -9.486832981 + 10 Combine like terms: -9.486832981 + 10 = 0.513167019 x2 = 0.513167019 Simplifying x2 = 0.513167019 Take the square root of each side: x = {-0.716356768, 0.716356768}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.41438931, 4.41438931, -0.716356768, 0.716356768}
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