6r^2=26-r

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Solution for 6r^2=26-r equation:


Simplifying
6r2 = 26 + -1r

Solving
6r2 = 26 + -1r

Solving for variable 'r'.

Reorder the terms:
-26 + r + 6r2 = 26 + -1r + -26 + r

Reorder the terms:
-26 + r + 6r2 = 26 + -26 + -1r + r

Combine like terms: 26 + -26 = 0
-26 + r + 6r2 = 0 + -1r + r
-26 + r + 6r2 = -1r + r

Combine like terms: -1r + r = 0
-26 + r + 6r2 = 0

Factor a trinomial.
(-13 + -6r)(2 + -1r) = 0

Subproblem 1

Set the factor '(-13 + -6r)' equal to zero and attempt to solve: Simplifying -13 + -6r = 0 Solving -13 + -6r = 0 Move all terms containing r to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -6r = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -6r = 0 + 13 -6r = 0 + 13 Combine like terms: 0 + 13 = 13 -6r = 13 Divide each side by '-6'. r = -2.166666667 Simplifying r = -2.166666667

Subproblem 2

Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 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 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2

Solution

r = {-2.166666667, 2}

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