Question

Solve using the quadratic formula.
-v^2 + 9v - 5 = 0​

Answer 1

v = 9/2 + sqrt(61)/2 or v = 9/2 - sqrt(61)/2

Explanation:

Solve for v over the real numbers:

-v^2 + 9 v - 5 = 0

Multiply both sides by -1:

v^2 - 9 v + 5 = 0

Subtract 5 from both sides:

v^2 - 9 v = -5

Add 81/4 to both sides:

v^2 - 9 v + 81/4 = 61/4

Write the left hand side as a square:

(v - 9/2)^2 = 61/4

Take the square root of both sides:

v - 9/2 = sqrt(61)/2 or v - 9/2 = -sqrt(61)/2

Add 9/2 to both sides:

v = 9/2 + sqrt(61)/2 or v - 9/2 = -sqrt(61)/2

Add 9/2 to both sides:

Answer: v = 9/2 + sqrt(61)/2 or v = 9/2 - sqrt(61)/2