63x^4-70x^2+15=0

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Solution for 63x^4-70x^2+15=0 equation:


Simplifying
63x4 + -70x2 + 15 = 0

Reorder the terms:
15 + -70x2 + 63x4 = 0

Solving
15 + -70x2 + 63x4 = 0

Solving for variable 'x'.

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

Divide each side by '63'.
0.2380952381 + -1.111111111x2 + x4 = 0

Move the constant term to the right:

Add '-0.2380952381' to each side of the equation.
0.2380952381 + -1.111111111x2 + -0.2380952381 + x4 = 0 + -0.2380952381

Reorder the terms:
0.2380952381 + -0.2380952381 + -1.111111111x2 + x4 = 0 + -0.2380952381

Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000
0.0000000000 + -1.111111111x2 + x4 = 0 + -0.2380952381
-1.111111111x2 + x4 = 0 + -0.2380952381

Combine like terms: 0 + -0.2380952381 = -0.2380952381
-1.111111111x2 + x4 = -0.2380952381

The x term is -1.111111111x2.  Take half its coefficient (-0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
-1.111111111x2 + 0.3086419752 + x4 = -0.2380952381 + 0.3086419752

Reorder the terms:
0.3086419752 + -1.111111111x2 + x4 = -0.2380952381 + 0.3086419752

Combine like terms: -0.2380952381 + 0.3086419752 = 0.0705467371
0.3086419752 + -1.111111111x2 + x4 = 0.0705467371

Factor a perfect square on the left side:
(x2 + -0.5555555555)(x2 + -0.5555555555) = 0.0705467371

Calculate the square root of the right side: 0.265606357

Break this problem into two subproblems by setting 
(x2 + -0.5555555555) equal to 0.265606357 and -0.265606357.

Subproblem 1

x2 + -0.5555555555 = 0.265606357 Simplifying x2 + -0.5555555555 = 0.265606357 Reorder the terms: -0.5555555555 + x2 = 0.265606357 Solving -0.5555555555 + x2 = 0.265606357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x2 = 0.265606357 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x2 = 0.265606357 + 0.5555555555 x2 = 0.265606357 + 0.5555555555 Combine like terms: 0.265606357 + 0.5555555555 = 0.8211619125 x2 = 0.8211619125 Simplifying x2 = 0.8211619125 Take the square root of each side: x = {-0.906179846, 0.906179846}

Subproblem 2

x2 + -0.5555555555 = -0.265606357 Simplifying x2 + -0.5555555555 = -0.265606357 Reorder the terms: -0.5555555555 + x2 = -0.265606357 Solving -0.5555555555 + x2 = -0.265606357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x2 = -0.265606357 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x2 = -0.265606357 + 0.5555555555 x2 = -0.265606357 + 0.5555555555 Combine like terms: -0.265606357 + 0.5555555555 = 0.2899491985 x2 = 0.2899491985 Simplifying x2 = 0.2899491985 Take the square root of each side: x = {-0.538469311, 0.538469311}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.906179846, 0.906179846, -0.538469311, 0.538469311}

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