16x^4=(65x^2)-49

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Solution for 16x^4=(65x^2)-49 equation: 


Simplifying
16x4 = (65x2) + -49

Reorder the terms:
16x4 = -49 + (65x2)

Solving
16x4 = -49 + (65x2)

Solving for variable 'x'.

Reorder the terms:
49 + (-65x2) + 16x4 = -49 + (65x2) + 49 + (-65x2)

Reorder the terms:
49 + (-65x2) + 16x4 = -49 + 49 + (65x2) + (-65x2)

Combine like terms: -49 + 49 = 0
49 + (-65x2) + 16x4 = 0 + (65x2) + (-65x2)
49 + (-65x2) + 16x4 = (65x2) + (-65x2)

Combine like terms: (65x2) + (-65x2) = 0
49 + (-65x2) + 16x4 = 0

Factor a trinomial.
(1 + -1x2)(49 + -16x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(49 + -16x2) = 0

Factor a difference between two squares.
((7 + 4x)(7 + -4x))(1 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 3
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75

Subproblem 4
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-1, 1, -1.75, 1.75}

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