(2x^2-8)(x^2-49)=0

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Solution for (2x^2-8)(x^2-49)=0 equation:


Simplifying
(2x2 + -8)(x2 + -49) = 0

Reorder the terms:
(-8 + 2x2)(x2 + -49) = 0

Reorder the terms:
(-8 + 2x2)(-49 + x2) = 0

Multiply (-8 + 2x2) * (-49 + x2)
(-8(-49 + x2) + 2x2 * (-49 + x2)) = 0
((-49 * -8 + x2 * -8) + 2x2 * (-49 + x2)) = 0
((392 + -8x2) + 2x2 * (-49 + x2)) = 0
(392 + -8x2 + (-49 * 2x2 + x2 * 2x2)) = 0
(392 + -8x2 + (-98x2 + 2x4)) = 0

Combine like terms: -8x2 + -98x2 = -106x2
(392 + -106x2 + 2x4) = 0

Solving
392 + -106x2 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(196 + -53x2 + x4) = 0

Factor a trinomial.
2((4 + -1x2)(49 + -1x2)) = 0

Factor a difference between two squares.
2(((2 + x)(2 + -1x))(49 + -1x2)) = 0

Factor a difference between two squares.
2(((7 + x)(7 + -1x))(2 + x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 3

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 4

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-2, 2, -7, 7}

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