2x^4=7x^2-15

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Solution for 2x^4=7x^2-15 equation:


Simplifying
2x4 = 7x2 + -15

Reorder the terms:
2x4 = -15 + 7x2

Solving
2x4 = -15 + 7x2

Solving for variable 'x'.

Reorder the terms:
15 + -7x2 + 2x4 = -15 + 7x2 + 15 + -7x2

Reorder the terms:
15 + -7x2 + 2x4 = -15 + 15 + 7x2 + -7x2

Combine like terms: -15 + 15 = 0
15 + -7x2 + 2x4 = 0 + 7x2 + -7x2
15 + -7x2 + 2x4 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
15 + -7x2 + 2x4 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
7.5 + -3.5x2 + x4 = 0

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + -3.5x2 + -7.5 + x4 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + -3.5x2 + x4 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + -3.5x2 + x4 = 0 + -7.5
-3.5x2 + x4 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
-3.5x2 + x4 = -7.5

The x term is -3.5x2.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x2 + 3.0625 + x4 = -7.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x2 + x4 = -7.5 + 3.0625

Combine like terms: -7.5 + 3.0625 = -4.4375
3.0625 + -3.5x2 + x4 = -4.4375

Factor a perfect square on the left side:
(x2 + -1.75)(x2 + -1.75) = -4.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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