How do you solve $5 p^{2} - 8 p = 0$ $5p ^ { 2} - 8p = 0$ ?

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How do you solve $5 p^{2} - 8 p = 0$ $5p ^ { 2} - 8p = 0$ ?

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Answer 1 · 2018-03-03T22:55:11

$p = 0$ $p=0$ and $p = \frac{8}{5}$ $p=8/5$

Explanation:

Both terms have a $p$ $p$ in common, so we can factor that out. We get:

$p (5 p - 8) = 0$ $p(5p-8)=0$

If the product of two things are equal to zero, either one or both of them must be equal to zero. So let's set them equal to zero. We get:

$p = 0$ $p=0$ , and for the term in parenthesis:

$5 p - 8 = 0$ $5p-8=0$

$5 p = 8$ $5p=8$

$p = \frac{8}{5}$ $p=8/5$

Therefore, our two zeroes are $p = 0$ $p=0$ and $p = \frac{8}{5}$ $p=8/5$

Answer 2 · 2018-03-03T23:07:22

$p = 0$ $p=0$ , or $p = \frac{8}{5}$ $p=8/5$

Explanation:

Step one is to factor the left side of the equation. You can factor out a $p$ $p$ from each term, giving you $p (5 p - 8) = 0$ $p(5p-8)=0$

From here, you can divide both sides by $p$ $p$ , or by $5 p - 8$ $5p-8$ . I'll start with dividing by $5 p - 8$ $5p-8$ . This gives us $p = 0$ $p=0$ . That's your first solution, but not the only one.

Next, we'll divide both sides by $p$ $p$ . This gives us $5 p - 8 = 0$ $5p-8=0$
Add $8$ $8$ to both side to get $5 p = 8$ $5p=8$
Divide both sides by $5$ $5$ , and we have our other solution $p = \frac{8}{5}$ $p=8/5$

You can check your work by plugging these values into your initial equation.
For $p = 0$ $p=0$ ,
$5 {(0)}^{2} - 8 (0) = 0$ $5(0)^2-8(0)=0$
$5 (0) - 0 = 0$ $5(0)-0=0$
$0 = 0$ $0=0$
So, $p = 0$ $p=0$ is correct.

For $p = \frac{8}{5}$ $p=8/5$ ,
$5 {(\frac{8}{5})}^{2} - 8 (\frac{8}{5}) = 0$ $5(8/5)^2-8(8/5)=0$
$5 (\frac{48}{25}) - \frac{48}{5} = 0$ $5(48/25)-48/5=0$
$\frac{48}{5} - \frac{48}{5} = 0$ $48/5-48/5=0$
$0 = 0$ $0=0$
So, $p = \frac{8}{5}$ $p=8/5$ is also correct.

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How do you solve $5 p^{2} - 8 p = 0$ $5p ^ { 2} - 8p = 0$ ?

2 Answers

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