2x^4-15x^2+12=0

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Solution for 2x^4-15x^2+12=0 equation:


Simplifying
2x4 + -15x2 + 12 = 0

Reorder the terms:
12 + -15x2 + 2x4 = 0

Solving
12 + -15x2 + 2x4 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
6 + -7.5x2 + x4 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -7.5x2 + -6 + x4 = 0 + -6

Reorder the terms:
6 + -6 + -7.5x2 + x4 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7.5x2 + x4 = 0 + -6
-7.5x2 + x4 = 0 + -6

Combine like terms: 0 + -6 = -6
-7.5x2 + x4 = -6

The x term is -7.5x2.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x2 + 14.0625 + x4 = -6 + 14.0625

Reorder the terms:
14.0625 + -7.5x2 + x4 = -6 + 14.0625

Combine like terms: -6 + 14.0625 = 8.0625
14.0625 + -7.5x2 + x4 = 8.0625

Factor a perfect square on the left side:
(x2 + -3.75)(x2 + -3.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x2 + -3.75) equal to 2.839454173 and -2.839454173.

Subproblem 1

x2 + -3.75 = 2.839454173 Simplifying x2 + -3.75 = 2.839454173 Reorder the terms: -3.75 + x2 = 2.839454173 Solving -3.75 + x2 = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x2 = 2.839454173 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x2 = 2.839454173 + 3.75 x2 = 2.839454173 + 3.75 Combine like terms: 2.839454173 + 3.75 = 6.589454173 x2 = 6.589454173 Simplifying x2 = 6.589454173 Take the square root of each side: x = {-2.566993216, 2.566993216}

Subproblem 2

x2 + -3.75 = -2.839454173 Simplifying x2 + -3.75 = -2.839454173 Reorder the terms: -3.75 + x2 = -2.839454173 Solving -3.75 + x2 = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x2 = -2.839454173 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x2 = -2.839454173 + 3.75 x2 = -2.839454173 + 3.75 Combine like terms: -2.839454173 + 3.75 = 0.910545827 x2 = 0.910545827 Simplifying x2 = 0.910545827 Take the square root of each side: x = {-0.95422525, 0.95422525}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.566993216, 2.566993216, -0.95422525, 0.95422525}

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