(7x^2-3)(7x^2-3)=0

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Solution for (7x^2-3)(7x^2-3)=0 equation:


Simplifying
(7x2 + -3)(7x2 + -3) = 0

Reorder the terms:
(-3 + 7x2)(7x2 + -3) = 0

Reorder the terms:
(-3 + 7x2)(-3 + 7x2) = 0

Multiply (-3 + 7x2) * (-3 + 7x2)
(-3(-3 + 7x2) + 7x2 * (-3 + 7x2)) = 0
((-3 * -3 + 7x2 * -3) + 7x2 * (-3 + 7x2)) = 0
((9 + -21x2) + 7x2 * (-3 + 7x2)) = 0
(9 + -21x2 + (-3 * 7x2 + 7x2 * 7x2)) = 0
(9 + -21x2 + (-21x2 + 49x4)) = 0

Combine like terms: -21x2 + -21x2 = -42x2
(9 + -42x2 + 49x4) = 0

Solving
9 + -42x2 + 49x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -7x2)(3 + -7x2) = 0

Subproblem 1

Set the factor '(3 + -7x2)' equal to zero and attempt to solve: Simplifying 3 + -7x2 = 0 Solving 3 + -7x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7x2 = 0 + -3 -7x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -7x2 = -3 Divide each side by '-7'. x2 = 0.4285714286 Simplifying x2 = 0.4285714286 Take the square root of each side: x = {-0.654653671, 0.654653671}

Subproblem 2

Set the factor '(3 + -7x2)' equal to zero and attempt to solve: Simplifying 3 + -7x2 = 0 Solving 3 + -7x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7x2 = 0 + -3 -7x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -7x2 = -3 Divide each side by '-7'. x2 = 0.4285714286 Simplifying x2 = 0.4285714286 Take the square root of each side: x = {-0.654653671, 0.654653671}

Solution

x = {-0.654653671, 0.654653671, -0.654653671, 0.654653671}

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