x^4-15x^2+9=0

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Solution for x^4-15x^2+9=0 equation:


Simplifying
x4 + -15x2 + 9 = 0

Reorder the terms:
9 + -15x2 + x4 = 0

Solving
9 + -15x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -15x2 + -9 + x4 = 0 + -9

Reorder the terms:
9 + -9 + -15x2 + x4 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -15x2 + x4 = 0 + -9
-15x2 + x4 = 0 + -9

Combine like terms: 0 + -9 = -9
-15x2 + x4 = -9

The x term is -15x2.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x2 + 56.25 + x4 = -9 + 56.25

Reorder the terms:
56.25 + -15x2 + x4 = -9 + 56.25

Combine like terms: -9 + 56.25 = 47.25
56.25 + -15x2 + x4 = 47.25

Factor a perfect square on the left side:
(x2 + -7.5)(x2 + -7.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(x2 + -7.5) equal to 6.873863542 and -6.873863542.

Subproblem 1

x2 + -7.5 = 6.873863542 Simplifying x2 + -7.5 = 6.873863542 Reorder the terms: -7.5 + x2 = 6.873863542 Solving -7.5 + x2 = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = 6.873863542 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 6.873863542 + 7.5 x2 = 6.873863542 + 7.5 Combine like terms: 6.873863542 + 7.5 = 14.373863542 x2 = 14.373863542 Simplifying x2 = 14.373863542 Take the square root of each side: x = {-3.791287847, 3.791287847}

Subproblem 2

x2 + -7.5 = -6.873863542 Simplifying x2 + -7.5 = -6.873863542 Reorder the terms: -7.5 + x2 = -6.873863542 Solving -7.5 + x2 = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = -6.873863542 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -6.873863542 + 7.5 x2 = -6.873863542 + 7.5 Combine like terms: -6.873863542 + 7.5 = 0.626136458 x2 = 0.626136458 Simplifying x2 = 0.626136458 Take the square root of each side: x = {-0.791287848, 0.791287848}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.791287847, 3.791287847, -0.791287848, 0.791287848}

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