Question

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

Answer 1

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)