49r^2=-24+77r

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Solution for 49r^2=-24+77r equation:


Simplifying
49r2 = -24 + 77r

Solving
49r2 = -24 + 77r

Solving for variable 'r'.

Reorder the terms:
24 + -77r + 49r2 = -24 + 77r + 24 + -77r

Reorder the terms:
24 + -77r + 49r2 = -24 + 24 + 77r + -77r

Combine like terms: -24 + 24 = 0
24 + -77r + 49r2 = 0 + 77r + -77r
24 + -77r + 49r2 = 77r + -77r

Combine like terms: 77r + -77r = 0
24 + -77r + 49r2 = 0

Factor a trinomial.
(3 + -7r)(8 + -7r) = 0

Subproblem 1

Set the factor '(3 + -7r)' equal to zero and attempt to solve: Simplifying 3 + -7r = 0 Solving 3 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7r = 0 + -3 -7r = 0 + -3 Combine like terms: 0 + -3 = -3 -7r = -3 Divide each side by '-7'. r = 0.4285714286 Simplifying r = 0.4285714286

Subproblem 2

Set the factor '(8 + -7r)' equal to zero and attempt to solve: Simplifying 8 + -7r = 0 Solving 8 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7r = 0 + -8 -7r = 0 + -8 Combine like terms: 0 + -8 = -8 -7r = -8 Divide each side by '-7'. r = 1.142857143 Simplifying r = 1.142857143

Solution

r = {0.4285714286, 1.142857143}

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