Question

3x^2+2root5x-5=0
Completing the square method
I am supposed to get answer as root 5/3

Answer 1

Answer:

x = ± $\frac{\sqrt{5} }{3}$

Step-by-step explanation:

Given

3x² + 2$\sqrt{5}$ x - 5 = 0 ( add 5 to both sides )

3x² + 2$\sqrt{5}$ x = 5

Before completing the square we require the coefficient of the x² term to be 1

Factor out 3 from each term on the left side

3(x² + $\frac{2\sqrt{5} }{3}$ x ) = 5

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + $\frac{2\sqrt{5} }{3}$ x

3(x² + 2( $\frac{\sqrt{5} }{3}$ )x + $\frac{5}{9}$ - $\frac{5}{9}$ ) = 5

3(x + $\frac{\sqrt{5} }{3}$ )² + ( 3 × - $\frac{5}{9}$ ) = 5

3(x + $\frac{\sqrt{5} }{3}$ )² - $\frac{5}{3}$ = 5 ( add $\frac{5}{3}$ to both sides )

3(x + $\frac{\sqrt{5} }{3}$ )² = $\frac{20}{3}$ ( divide both sides by 3 )

(x + $\frac{\sqrt{5} }{3}$ )² = $\frac{20}{9}$ ( take the square root of both sides )

x + $\frac{\sqrt{5} }{3}$ = ± $\sqrt{\frac{20}{9} }$ = ± $\frac{2\sqrt{5} }{3}$ ( subtract $\frac{\sqrt{5} }{3}$ from both sides )

x = - $\frac{\sqrt{5} }{3}$ ± $\frac{2\sqrt{5} }{3}$

Thus

x = - $\frac{\sqrt{5} }{3}$ - $\frac{2\sqrt{5} }{3}$ = - $\frac{\sqrt{5} }{3}$

x = - $\frac{\sqrt{5} }{3}$ +$\frac{2\sqrt{5} }{3}$ = $\frac{\sqrt{5} }{3}$