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

2 Answers
Jacobi J.
Mar 3, 2018

#p=0# and #p=8/5#

Explanation:

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

#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#, and for the term in parenthesis:

#5p-8=0#

#5p=8#

#p=8/5#

Therefore, our two zeroes are #p=0# and #p=8/5#

Zach J.
Mar 3, 2018

#p=0#, or #p=8/5#

Explanation:

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

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

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

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

For #p=8/5#,
#5(8/5)^2-8(8/5)=0#
#5(48/25)-48/5=0#
#48/5-48/5=0#
#0=0#
So, #p=8/5# is also correct.

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