10q^2-29qr+10r^2=

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Solution for 10q^2-29qr+10r^2= equation:


Simplifying
10q2 + -29qr + 10r2 = 0

Reorder the terms:
-29qr + 10q2 + 10r2 = 0

Solving
-29qr + 10q2 + 10r2 = 0

Solving for variable 'q'.

Factor a trinomial.
(2q + -5r)(5q + -2r) = 0

Subproblem 1

Set the factor '(2q + -5r)' equal to zero and attempt to solve: Simplifying 2q + -5r = 0 Solving 2q + -5r = 0 Move all terms containing q to the left, all other terms to the right. Add '5r' to each side of the equation. 2q + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 2q + 0 = 0 + 5r 2q = 0 + 5r Remove the zero: 2q = 5r Divide each side by '2'. q = 2.5r Simplifying q = 2.5r

Subproblem 2

Set the factor '(5q + -2r)' equal to zero and attempt to solve: Simplifying 5q + -2r = 0 Solving 5q + -2r = 0 Move all terms containing q to the left, all other terms to the right. Add '2r' to each side of the equation. 5q + -2r + 2r = 0 + 2r Combine like terms: -2r + 2r = 0 5q + 0 = 0 + 2r 5q = 0 + 2r Remove the zero: 5q = 2r Divide each side by '5'. q = 0.4r Simplifying q = 0.4r

Solution

q = {2.5r, 0.4r}

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