x^4-15x^2+16=0

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Solution for x^4-15x^2+16=0 equation:


Simplifying
x4 + -15x2 + 16 = 0

Reorder the terms:
16 + -15x2 + x4 = 0

Solving
16 + -15x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -15x2 + -16 + x4 = 0 + -16

Reorder the terms:
16 + -16 + -15x2 + x4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -15x2 + x4 = 0 + -16
-15x2 + x4 = 0 + -16

Combine like terms: 0 + -16 = -16
-15x2 + x4 = -16

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 = -16 + 56.25

Reorder the terms:
56.25 + -15x2 + x4 = -16 + 56.25

Combine like terms: -16 + 56.25 = 40.25
56.25 + -15x2 + x4 = 40.25

Factor a perfect square on the left side:
(x2 + -7.5)(x2 + -7.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x2 + -7.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

x2 + -7.5 = 6.34428877 Simplifying x2 + -7.5 = 6.34428877 Reorder the terms: -7.5 + x2 = 6.34428877 Solving -7.5 + x2 = 6.34428877 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 = 6.34428877 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 6.34428877 + 7.5 x2 = 6.34428877 + 7.5 Combine like terms: 6.34428877 + 7.5 = 13.84428877 x2 = 13.84428877 Simplifying x2 = 13.84428877 Take the square root of each side: x = {-3.720791417, 3.720791417}

Subproblem 2

x2 + -7.5 = -6.34428877 Simplifying x2 + -7.5 = -6.34428877 Reorder the terms: -7.5 + x2 = -6.34428877 Solving -7.5 + x2 = -6.34428877 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 = -6.34428877 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -6.34428877 + 7.5 x2 = -6.34428877 + 7.5 Combine like terms: -6.34428877 + 7.5 = 1.15571123 x2 = 1.15571123 Simplifying x2 = 1.15571123 Take the square root of each side: x = {-1.075040106, 1.075040106}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.720791417, 3.720791417, -1.075040106, 1.075040106}

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