Question

please help a girl out

Answer 1

Answer:

$r=\frac{7±3\sqrt{5} }{2}$

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

Step-by-step 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

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

$r=\frac{-(-7)±\sqrt{49-4((1)(1)) } }{2(1)}$

$r=\frac{-(-7)±\sqrt{49-4 } }{2(1)}$

$r=\frac{-(-7)±\sqrt{45 } }{2(1)}$

$r=\frac{-(-7)±\sqrt{(3)(3)(5) } }{2(1)}$

$r=\frac{7±(\sqrt{3 } )(\sqrt{3})(\sqrt{5}) }{2(1)}$

$r=\frac{7±3\sqrt{5} }{2}$

Two separate equations

$r=\frac{7+3\sqrt{5} }{2}$

$r=\frac{7-3\sqrt{5} }{2}$