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Simplifying 100 = (x2)(x2 + 2) Reorder the terms: 100 = x2(2 + x2) 100 = (2 * x2 + x2 * x2) 100 = (2x2 + x4) Solving 100 = 2x2 + x4 Solving for variable 'x'. Reorder the terms: 100 + -2x2 + -1x4 = 2x2 + -2x2 + x4 + -1x4 Combine like terms: 2x2 + -2x2 = 0 100 + -2x2 + -1x4 = 0 + x4 + -1x4 100 + -2x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 100 + -2x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 2x2 + x4 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 2x2 + 100 + x4 = 0 + 100 Reorder the terms: -100 + 100 + 2x2 + x4 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 2x2 + x4 = 0 + 100 2x2 + x4 = 0 + 100 Combine like terms: 0 + 100 = 100 2x2 + x4 = 100 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 100 + 1 Reorder the terms: 1 + 2x2 + x4 = 100 + 1 Combine like terms: 100 + 1 = 101 1 + 2x2 + x4 = 101 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x2 + 1) equal to 10.049875621 and -10.049875621.Subproblem 1
x2 + 1 = 10.049875621 Simplifying x2 + 1 = 10.049875621 Reorder the terms: 1 + x2 = 10.049875621 Solving 1 + x2 = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 10.049875621 + -1 x2 = 10.049875621 + -1 Combine like terms: 10.049875621 + -1 = 9.049875621 x2 = 9.049875621 Simplifying x2 = 9.049875621 Take the square root of each side: x = {-3.008301119, 3.008301119}Subproblem 2
x2 + 1 = -10.049875621 Simplifying x2 + 1 = -10.049875621 Reorder the terms: 1 + x2 = -10.049875621 Solving 1 + x2 = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -10.049875621 + -1 x2 = -10.049875621 + -1 Combine like terms: -10.049875621 + -1 = -11.049875621 x2 = -11.049875621 Simplifying x2 = -11.049875621 Reorder the terms: 11.049875621 + x2 = -11.049875621 + 11.049875621 Combine like terms: -11.049875621 + 11.049875621 = 0.000000000 11.049875621 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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