Factor by completing the square 5x^2-21=10x

Solve for x over the real numbers:

5 x^2 - 21 = 10 x

Subtract 10 x from both sides:

5 x^2 - 10 x - 21 = 0

Divide both sides by 5:

x^2 - 2 x - 21/5 = 0

Add 21/5 to both sides:

x^2 - 2 x = 21/5

Add 1 to both sides:

x^2 - 2 x + 1 = 26/5

Write the left hand side as a square:

(x - 1) ^2 = 26/5

Take the square root of both sides:

x - 1 = sqrt (26/5) or x - 1 = - sqrt (26/5)

Add 1 to both sides:

x = 1 + sqrt (26/5) or x - 1 = - sqrt (26/5)

Add 1 to both sides:

Answer: x = 1 + sqrt (26/5) or x = 1 - sqrt (26/5)