Solve the equation.
2^3square root 5m+5 +7=5

Question

Solve the equation.
2^3square root 5m+5 +7=5

wckeller · Answer

Can you use the equation button below to show your problem? It's kind of difficult to understand where the square root stops.

lolaus · Answer

$$2^{3}\sqrt{5m+4}+7=5$$

wckeller · Answer

is it 5m+4 or 5m+5 because in the first representation of the equation you said it was a +5

wckeller · Answer

Oh! By the way, welcome to Open Study!

lolaus · Answer

my bad the right question is 5m+4

wckeller · Answer

Okay.
So to solve for M we need to get it all alone on one side of the equation.
First we can start by subtracting a 7 from both sides.

lolaus · Answer

thank you appreciated.

wckeller · Answer

$$2^3 \sqrt{5m+4}=5-7$$

wckeller · Answer

$$2^3 \sqrt{5m+4}=-2$$

wckeller · Answer

$$2^3 = 8$$
$$8\sqrt{5m+4}=-2$$

wckeller · Answer

Divide both sides by 8

wckeller · Answer

$$\sqrt{5m+4}=\frac{ -2 }{ 8 }$$

wckeller · Answer

Now in order to get rid of the square root, we need to square both sides.

wckeller · Answer

$$\sqrt{5m+4}^2=(\frac{ -2 }{ 8 })^2$$
$$5m+4=\frac{ 4 }{ 64 }$$
$$\frac{ 4 }{ 64 } = \frac{ 1 }{ 16 }$$
$$5m+4=\frac{ 1 }{ 16 }$$

wckeller · Answer

Now we need to subtract 4 from both sides.

wckeller · Answer

$$5m=\frac{ 1 }{ 16 }-4$$
Find a common denominator for 4 and 1/16
$$4=\frac{ 64 }{ 16 }$$
$$5m=\frac{ 1 }{ 16 }-\frac{ 64 }{ 16 }$$

wckeller · Answer

$$1-64=-63$$
$$5m=\frac{ -63 }{ 16 }$$
Now we need to divide both sides by 5.
$$m=\frac{ \frac{ -63 }{ 16 } }{ 5 }$$
Which is the same as $$m=\frac{ -63 }{ 16*5 }$$
$$m=\frac{ -63 }{ 80 }$$

Final answer:
$$m=\frac{ -63 }{ 80 }$$

wckeller · Answer

I may have messed up somewhere, let me plug back in and check my work.

lolaus · Answer

Thank you Wckeller I really appreciate your kind help.

wckeller · Answer

Okay, I am SO sorry... I have royally messed up somewhere.

wckeller · Answer

The answer I'm getting when I plug back in is 9.

wckeller · Answer

But its supposed to be 5... let me find where I messed up.

wckeller · Answer

Oh boy, ive really messed up somewhere

wckeller · Answer

I found it.. So there is NO answer to this problem. A square root cannot equal a negative number.

wckeller · Answer

$$\sqrt{5m+4}=\frac{ -2 }{ 8 }$$
This is where the problem occurs.

wckeller · Answer

So the answer to this problem is: No Solution