How do you solve $5 r + 3 = 2 r^{2}$ $5r+3=2r^2$ ?

Question

How do you solve $5 r + 3 = 2 r^{2}$ $5r+3=2r^2$ ?

2 Answers

Impact of this question

2699 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-08T15:19:42

$r_{1} = - \frac{1}{2}$ $r_1=-1/2$ and $r_{2} = 3$ $r_2=3$

Explanation:

$5 r + 3 = 2 r^{2}$ $5r+3=2r^2$

$2 r^{2} - 5 r - 3 = 0$ $2r^2-5r-3=0$

$(2 r + 1) \cdot (r - 3) = 0$ $(2r+1)*(r-3)=0$

So $r_{1} = - \frac{1}{2}$ $r_1=-1/2$ and $r_{2} = 3$ $r_2=3$

Answer 2 · 2018-08-08T17:23:18

$r = - \frac{1}{2} or r = 3$ $r=-1/2" or "r=3$

Explanation:

$rearrange into standard form; a x^{2} + b x + c = 0; a \neq 0$ $"rearrange into standard form ";ax^2+bx+c=0;a!=0$

$subtract 5 r + 3 from both sides$ $"subtract "5r+3" from both sides"$

$2 r^{2} - 5 r - 3 = 0$ $2r^2-5r-3=0$

$factor using the a-c method$ $"factor using the a-c method"$

$the factors of the product 2 \times - 3 = - 6$ $"the factors of the product "2xx-3=-6$

$which sum to - 5 are - 6 and + 1$ $"which sum to "-5" are "-6" and "+1$

$split the middle term using these factors$ $"split the middle term using these factors"$

$2 r^{2} - 6 r + r - 3 = 0 \leftarrow factor by grouping$ $2r^2-6r+r-3=0larrcolor(blue)"factor by grouping"$

$2 r (r - 3) + 1 (r - 3) = 0$ $color(red)(2r)(r-3)color(red)(+1)(r-3)=0$

$take out the common factor (r - 3)$ $"take out the "color(blue)"common factor "(r-3)$

$(r - 3) (2 r + 1) = 0$ $(r-3)(color(red)(2r+1))=0$

$equate each factor to zero and solve for r$ $"equate each factor to zero and solve for r"$

$2 r + 1 = 0 \Rightarrow r = - \frac{1}{2}$ $2r+1=0rArrr=-1/2$

$r - 3 = 0 \Rightarrow r = 3$ $r-3=0rArrr=3$

Science

Math

Humanities

... and beyond

How do you solve $5 r + 3 = 2 r^{2}$ $5r+3=2r^2$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve 5r+3=2r25r+3=2r^2?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you solve $5 r + 3 = 2 r^{2}$ $5r+3=2r^2$ ?