49b^4-14b^2+1=0

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Solution for 49b^4-14b^2+1=0 equation:


Simplifying
49b4 + -14b2 + 1 = 0

Reorder the terms:
1 + -14b2 + 49b4 = 0

Solving
1 + -14b2 + 49b4 = 0

Solving for variable 'b'.

Factor a trinomial.
(1 + -7b2)(1 + -7b2) = 0

Subproblem 1

Set the factor '(1 + -7b2)' equal to zero and attempt to solve: Simplifying 1 + -7b2 = 0 Solving 1 + -7b2 = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -7b2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7b2 = 0 + -1 -7b2 = 0 + -1 Combine like terms: 0 + -1 = -1 -7b2 = -1 Divide each side by '-7'. b2 = 0.1428571429 Simplifying b2 = 0.1428571429 Take the square root of each side: b = {-0.377964473, 0.377964473}

Subproblem 2

Set the factor '(1 + -7b2)' equal to zero and attempt to solve: Simplifying 1 + -7b2 = 0 Solving 1 + -7b2 = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -7b2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7b2 = 0 + -1 -7b2 = 0 + -1 Combine like terms: 0 + -1 = -1 -7b2 = -1 Divide each side by '-7'. b2 = 0.1428571429 Simplifying b2 = 0.1428571429 Take the square root of each side: b = {-0.377964473, 0.377964473}

Solution

b = {-0.377964473, 0.377964473, -0.377964473, 0.377964473}

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