Question

What is the positive solution to this equation? 12x²-10x=65

Answer 1

`x = (√(805) + 5)/(12)\approx 2.78`

Explanation:

Solve for x by completing the square:

12x²-10x=65

• dividing both sides by 12

x² - (5/6)x = 65/12

• adding 25/144 [ (5/12)² ] to both sides

x² - (5/6)x + 25/144 = 65/12 + 25/144

• factoring the right side as a square

(x - 5/12)² = 65/12 + 25/144

• getting a common denominator on the right side

(x - 5/12)² = 780/144 + 25/144

• combining the fractions on the right side

(x - 5/12)² = 805/144

• square-rooting both sides

x - 5/12 = ±√(805/144)

• simplifying the square-rooted fraction

x - 5/12 = ±√(805)/12

• adding 5/12 to both sides

`x = (\pm√(805) + 5)/(12)`

• taking the positive solution

`\boxed{x = (√(805) + 5)/(12)}`