2х^4+5х^3+6х^2+5х+2=0

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To solve this equation, we can use the factoring method or use the numerical methods such as the quadratic formula or graphing.

One way to solve this equation is to factor it:

2x^4 + 5x^3 + 6x^2 + 5x + 2 = 0

This polynomial cannot be factored easily, so we can try finding the roots using numerical methods.

Using the quadratic formula:

The general form of a quadratic equation is ax^2 + bx + c = 0. In this case, we can consider the equation as a quadratic in terms of x^2:

let y = x^2

2y^2 + 5y + 6y + 2 = 0
2y^2 + 11y + 2 = 0

Now we can use the quadratic formula to solve for y:

y = [-b ± √(b^2 - 4ac)] / 2a

y = [-11 ± √(11^2 - 422)] / 2*2
y = [-11 ± √(121 - 16)] / 4
y = [-11 ± √105] / 4

Now, we can substitute back y = x^2:

x^2 = [-11 ± √105] / 4

Therefore, the solution to the equation 2x^4 + 5x^3 + 6x^2 + 5x + 2 = 0 is:

x = ±√([-11 ± √105] / 4)