(r+3)(r+3)=10r

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Solution for (r+3)(r+3)=10r equation:


Simplifying
(r + 3)(r + 3) = 10r

Reorder the terms:
(3 + r)(r + 3) = 10r

Reorder the terms:
(3 + r)(3 + r) = 10r

Multiply (3 + r) * (3 + r)
(3(3 + r) + r(3 + r)) = 10r
((3 * 3 + r * 3) + r(3 + r)) = 10r
((9 + 3r) + r(3 + r)) = 10r
(9 + 3r + (3 * r + r * r)) = 10r
(9 + 3r + (3r + r2)) = 10r

Combine like terms: 3r + 3r = 6r
(9 + 6r + r2) = 10r

Solving
9 + 6r + r2 = 10r

Solving for variable 'r'.

Reorder the terms:
9 + 6r + -10r + r2 = 10r + -10r

Combine like terms: 6r + -10r = -4r
9 + -4r + r2 = 10r + -10r

Combine like terms: 10r + -10r = 0
9 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -4r + -9 + r2 = 0 + -9

Reorder the terms:
9 + -9 + -4r + r2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4r + r2 = 0 + -9
-4r + r2 = 0 + -9

Combine like terms: 0 + -9 = -9
-4r + r2 = -9

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = -9 + 4

Reorder the terms:
4 + -4r + r2 = -9 + 4

Combine like terms: -9 + 4 = -5
4 + -4r + r2 = -5

Factor a perfect square on the left side:
(r + -2)(r + -2) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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