Question

Please help a girl out

Answer 1

`r=(7±3√(5) )/(2)`

Ignore the A before the ±. It wouldn't let me type it correctly.

Explanation:

2r² + 7r - 1 = 3r²

2r² + 7r - 1 - 3r² = 0

- r² + 7r - 1 = 0

- (r² - 7r + 1) = 0

- (r² - 7r + 1) ÷ - 1 = 0 ÷ - 1

r² - 7r + 1 = 0

`r=\frac{-b±\sqrt{b^(2)-4ac } }{2a}`

Ignore the A before the ±. It wouldn't let me type it correctly.

r² - 7r + 1 = 0

a = 1

b = - 7

c = 1

`r=\frac{-(-7)±\sqrt{(-7)^(2)-4((1)(1)) } }{2(1)}`

`r=(-(-7)±√(49-4((1)(1)) ) )/(2(1))`

`r=(-(-7)±√(49-4 ) )/(2(1))`

`r=(-(-7)±√(45 ) )/(2(1))`

`r=(-(-7)±√((3)(3)(5) ) )/(2(1))`

`r=(7±(√(3 ) )(√(3))(√(5)) )/(2(1))`

`r=(7±3√(5) )/(2)`

Two separate equations

`r=(7+3√(5) )/(2)`

`r=(7-3√(5) )/(2)`