x^4-49x^2=7

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Solution for x^4-49x^2=7 equation: 


Simplifying
x4 + -49x2 = 7

Reorder the terms:
-49x2 + x4 = 7

Solving
-49x2 + x4 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + -49x2 + x4 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -49x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -49x2 + 7 + x4 = 0 + 7

Reorder the terms:
-7 + 7 + -49x2 + x4 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -49x2 + x4 = 0 + 7
-49x2 + x4 = 0 + 7

Combine like terms: 0 + 7 = 7
-49x2 + x4 = 7

The x term is -49x2.  Take half its coefficient (-24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
-49x2 + 600.25 + x4 = 7 + 600.25

Reorder the terms:
600.25 + -49x2 + x4 = 7 + 600.25

Combine like terms: 7 + 600.25 = 607.25
600.25 + -49x2 + x4 = 607.25

Factor a perfect square on the left side:
(x2 + -24.5)(x2 + -24.5) = 607.25

Calculate the square root of the right side: 24.642443061

Break this problem into two subproblems by setting 
(x2 + -24.5) equal to 24.642443061 and -24.642443061.


Subproblem 1
x2 + -24.5 = 24.642443061

Simplifying
x2 + -24.5 = 24.642443061

Reorder the terms:
-24.5 + x2 = 24.642443061

Solving
-24.5 + x2 = 24.642443061

Solving for variable 'x'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + x2 = 24.642443061 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x2 = 24.642443061 + 24.5
x2 = 24.642443061 + 24.5

Combine like terms: 24.642443061 + 24.5 = 49.142443061
x2 = 49.142443061

Simplifying
x2 = 49.142443061

Take the square root of each side:
x = {-7.010167121, 7.010167121}


Subproblem 2
x2 + -24.5 = -24.642443061

Simplifying
x2 + -24.5 = -24.642443061

Reorder the terms:
-24.5 + x2 = -24.642443061

Solving
-24.5 + x2 = -24.642443061

Solving for variable 'x'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + x2 = -24.642443061 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x2 = -24.642443061 + 24.5
x2 = -24.642443061 + 24.5

Combine like terms: -24.642443061 + 24.5 = -0.142443061
x2 = -0.142443061

Simplifying
x2 = -0.142443061

Reorder the terms:
0.142443061 + x2 = -0.142443061 + 0.142443061

Combine like terms: -0.142443061 + 0.142443061 = 0.000000000
0.142443061 + x2 = 0.000000000

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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