4x^4+7x^2-6=0

Solution for 4x^4+7x^2-6=0 equation:

Simplifying
4x4 + 7x2 + -6 = 0

Reorder the terms:
-6 + 7x2 + 4x4 = 0

Solving
-6 + 7x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1.5 + 1.75x2 + x4 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.75x2 + 1.5 + x4 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.75x2 + x4 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.75x2 + x4 = 0 + 1.5
1.75x2 + x4 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.75x2 + x4 = 1.5

The x term is 1.75x2.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x2 + 0.765625 + x4 = 1.5 + 0.765625

Reorder the terms:
0.765625 + 1.75x2 + x4 = 1.5 + 0.765625

Combine like terms: 1.5 + 0.765625 = 2.265625
0.765625 + 1.75x2 + x4 = 2.265625

Factor a perfect square on the left side:
(x2 + 0.875)(x2 + 0.875) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(x2 + 0.875) equal to 1.505199322 and -1.505199322.

Subproblem 1
x2 + 0.875 = 1.505199322

Simplifying
x2 + 0.875 = 1.505199322

Reorder the terms:
0.875 + x2 = 1.505199322

Solving
0.875 + x2 = 1.505199322

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x2 = 1.505199322 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x2 = 1.505199322 + -0.875
x2 = 1.505199322 + -0.875

Combine like terms: 1.505199322 + -0.875 = 0.630199322
x2 = 0.630199322

Simplifying
x2 = 0.630199322

Take the square root of each side:
x = {-0.793850944, 0.793850944}

Subproblem 2
x2 + 0.875 = -1.505199322

Simplifying
x2 + 0.875 = -1.505199322

Reorder the terms:
0.875 + x2 = -1.505199322

Solving
0.875 + x2 = -1.505199322

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x2 = -1.505199322 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x2 = -1.505199322 + -0.875
x2 = -1.505199322 + -0.875

Combine like terms: -1.505199322 + -0.875 = -2.380199322
x2 = -2.380199322

Simplifying
x2 = -2.380199322

Reorder the terms:
2.380199322 + x2 = -2.380199322 + 2.380199322

Combine like terms: -2.380199322 + 2.380199322 = 0.000000000
2.380199322 + 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.