x^4-14*x^2+28.95=0

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Solution for x^4-14*x^2+28.95=0 equation:


Simplifying
x4 + -14x2 + 28.95 = 0

Reorder the terms:
28.95 + -14x2 + x4 = 0

Solving
28.95 + -14x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-28.95' to each side of the equation.
28.95 + -14x2 + -28.95 + x4 = 0 + -28.95

Reorder the terms:
28.95 + -28.95 + -14x2 + x4 = 0 + -28.95

Combine like terms: 28.95 + -28.95 = 0.00
0.00 + -14x2 + x4 = 0 + -28.95
-14x2 + x4 = 0 + -28.95

Combine like terms: 0 + -28.95 = -28.95
-14x2 + x4 = -28.95

The x term is -14x2.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x2 + 49 + x4 = -28.95 + 49

Reorder the terms:
49 + -14x2 + x4 = -28.95 + 49

Combine like terms: -28.95 + 49 = 20.05
49 + -14x2 + x4 = 20.05

Factor a perfect square on the left side:
(x2 + -7)(x2 + -7) = 20.05

Calculate the square root of the right side: 4.477722635

Break this problem into two subproblems by setting 
(x2 + -7) equal to 4.477722635 and -4.477722635.

Subproblem 1

x2 + -7 = 4.477722635 Simplifying x2 + -7 = 4.477722635 Reorder the terms: -7 + x2 = 4.477722635 Solving -7 + x2 = 4.477722635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 4.477722635 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 4.477722635 + 7 x2 = 4.477722635 + 7 Combine like terms: 4.477722635 + 7 = 11.477722635 x2 = 11.477722635 Simplifying x2 = 11.477722635 Take the square root of each side: x = {-3.387878781, 3.387878781}

Subproblem 2

x2 + -7 = -4.477722635 Simplifying x2 + -7 = -4.477722635 Reorder the terms: -7 + x2 = -4.477722635 Solving -7 + x2 = -4.477722635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -4.477722635 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -4.477722635 + 7 x2 = -4.477722635 + 7 Combine like terms: -4.477722635 + 7 = 2.522277365 x2 = 2.522277365 Simplifying x2 = 2.522277365 Take the square root of each side: x = {-1.588167927, 1.588167927}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.387878781, 3.387878781, -1.588167927, 1.588167927}

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