8+6r^2-5r^4=0

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Solution for 8+6r^2-5r^4=0 equation:


Simplifying
8 + 6r2 + -5r4 = 0

Solving
8 + 6r2 + -5r4 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + -1r2)(4 + 5r2) = 0

Subproblem 1

Set the factor '(2 + -1r2)' equal to zero and attempt to solve: Simplifying 2 + -1r2 = 0 Solving 2 + -1r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r2 = 0 + -2 -1r2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1r2 = -2 Divide each side by '-1'. r2 = 2 Simplifying r2 = 2 Take the square root of each side: r = {-1.414213562, 1.414213562}

Subproblem 2

Set the factor '(4 + 5r2)' equal to zero and attempt to solve: Simplifying 4 + 5r2 = 0 Solving 4 + 5r2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5r2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5r2 = 0 + -4 5r2 = 0 + -4 Combine like terms: 0 + -4 = -4 5r2 = -4 Divide each side by '5'. r2 = -0.8 Simplifying r2 = -0.8 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

r = {-1.414213562, 1.414213562}

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