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Simplifying 1 + -4x2 + -9x4 = 0 Solving 1 + -4x2 + -9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.1111111111 + 0.4444444444x2 + x4 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.4444444444x2 + 0.1111111111 + x4 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.4444444444x2 + x4 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.4444444444x2 + x4 = 0 + 0.1111111111 0.4444444444x2 + x4 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.4444444444x2 + x4 = 0.1111111111 The x term is 0.4444444444x2. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x2 + 0.04938271604 + x4 = 0.1111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x2 + x4 = 0.1111111111 + 0.04938271604 Combine like terms: 0.1111111111 + 0.04938271604 = 0.16049382714 0.04938271604 + 0.4444444444x2 + x4 = 0.16049382714 Factor a perfect square on the left side: (x2 + 0.2222222222)(x2 + 0.2222222222) = 0.16049382714 Calculate the square root of the right side: 0.400616808 Break this problem into two subproblems by setting (x2 + 0.2222222222) equal to 0.400616808 and -0.400616808.Subproblem 1
x2 + 0.2222222222 = 0.400616808 Simplifying x2 + 0.2222222222 = 0.400616808 Reorder the terms: 0.2222222222 + x2 = 0.400616808 Solving 0.2222222222 + x2 = 0.400616808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x2 = 0.400616808 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x2 = 0.400616808 + -0.2222222222 x2 = 0.400616808 + -0.2222222222 Combine like terms: 0.400616808 + -0.2222222222 = 0.1783945858 x2 = 0.1783945858 Simplifying x2 = 0.1783945858 Take the square root of each side: x = {-0.422367832, 0.422367832}Subproblem 2
x2 + 0.2222222222 = -0.400616808 Simplifying x2 + 0.2222222222 = -0.400616808 Reorder the terms: 0.2222222222 + x2 = -0.400616808 Solving 0.2222222222 + x2 = -0.400616808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x2 = -0.400616808 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x2 = -0.400616808 + -0.2222222222 x2 = -0.400616808 + -0.2222222222 Combine like terms: -0.400616808 + -0.2222222222 = -0.6228390302 x2 = -0.6228390302 Simplifying x2 = -0.6228390302 Reorder the terms: 0.6228390302 + x2 = -0.6228390302 + 0.6228390302 Combine like terms: -0.6228390302 + 0.6228390302 = 0.0000000000 0.6228390302 + x2 = 0.0000000000 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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