11x^2+3=5(16x^4-9)

Solution for 11x^2+3=5(16x^4-9) equation:

Simplifying
11x2 + 3 = 5(16x4 + -9)

Reorder the terms:
3 + 11x2 = 5(16x4 + -9)

Reorder the terms:
3 + 11x2 = 5(-9 + 16x4)
3 + 11x2 = (-9 * 5 + 16x4 * 5)
3 + 11x2 = (-45 + 80x4)

Solving
3 + 11x2 = -45 + 80x4

Solving for variable 'x'.

Reorder the terms:
3 + 45 + 11x2 + -80x4 = -45 + 80x4 + 45 + -80x4

Combine like terms: 3 + 45 = 48
48 + 11x2 + -80x4 = -45 + 80x4 + 45 + -80x4

Reorder the terms:
48 + 11x2 + -80x4 = -45 + 45 + 80x4 + -80x4

Combine like terms: -45 + 45 = 0
48 + 11x2 + -80x4 = 0 + 80x4 + -80x4
48 + 11x2 + -80x4 = 80x4 + -80x4

Combine like terms: 80x4 + -80x4 = 0
48 + 11x2 + -80x4 = 0

Begin completing the square.  Divide all terms by
-80 the coefficient of the squared term: 

Divide each side by '-80'.
-0.6 + -0.1375x2 + x4 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.1375x2 + 0.6 + x4 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.1375x2 + x4 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.1375x2 + x4 = 0 + 0.6
-0.1375x2 + x4 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.1375x2 + x4 = 0.6

The x term is -0.1375x2.  Take half its coefficient (-0.06875).
Square it (0.0047265625) and add it to both sides.

Add '0.0047265625' to each side of the equation.
-0.1375x2 + 0.0047265625 + x4 = 0.6 + 0.0047265625

Reorder the terms:
0.0047265625 + -0.1375x2 + x4 = 0.6 + 0.0047265625

Combine like terms: 0.6 + 0.0047265625 = 0.6047265625
0.0047265625 + -0.1375x2 + x4 = 0.6047265625

Factor a perfect square on the left side:
(x2 + -0.06875)(x2 + -0.06875) = 0.6047265625

Calculate the square root of the right side: 0.777641667

Break this problem into two subproblems by setting 
(x2 + -0.06875) equal to 0.777641667 and -0.777641667.

Subproblem 1
x2 + -0.06875 = 0.777641667

Simplifying
x2 + -0.06875 = 0.777641667

Reorder the terms:
-0.06875 + x2 = 0.777641667

Solving
-0.06875 + x2 = 0.777641667

Solving for variable 'x'.

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

Add '0.06875' to each side of the equation.
-0.06875 + 0.06875 + x2 = 0.777641667 + 0.06875

Combine like terms: -0.06875 + 0.06875 = 0.00000
0.00000 + x2 = 0.777641667 + 0.06875
x2 = 0.777641667 + 0.06875

Combine like terms: 0.777641667 + 0.06875 = 0.846391667
x2 = 0.846391667

Simplifying
x2 = 0.846391667

Take the square root of each side:
x = {-0.919995471, 0.919995471}

Subproblem 2
x2 + -0.06875 = -0.777641667

Simplifying
x2 + -0.06875 = -0.777641667

Reorder the terms:
-0.06875 + x2 = -0.777641667

Solving
-0.06875 + x2 = -0.777641667

Solving for variable 'x'.

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

Add '0.06875' to each side of the equation.
-0.06875 + 0.06875 + x2 = -0.777641667 + 0.06875

Combine like terms: -0.06875 + 0.06875 = 0.00000
0.00000 + x2 = -0.777641667 + 0.06875
x2 = -0.777641667 + 0.06875

Combine like terms: -0.777641667 + 0.06875 = -0.708891667
x2 = -0.708891667

Simplifying
x2 = -0.708891667

Reorder the terms:
0.708891667 + x2 = -0.708891667 + 0.708891667

Combine like terms: -0.708891667 + 0.708891667 = 0.000000000
0.708891667 + 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.