Solve the equation for P

Question

Solve G = mP^2 + 10P for P

P= ___________

Answer 1

Oziel T's answer is not correct. He (or she) is doing this:

G = mP² + 10P

G = P(mP + 10)

G = P or G = mP + 10

However, that last step is only correct if G = 0. Unfortunately, we do not know that G = 0. Instead, you should recognize that this is a quadratic equation with P as the variable and therefore solve it as a quadratic equation. To do so correctly, move everything onto one side of the equation (leaving 0 on the other side) and then use the quadratic formula:

G = mP² + 10P

mP² + 10P - G = 0

P = (-10 +/- sqrt(10² - 4m(-G)))/2m

P = (-10 +/- sqrt(100 + 4mG))/2m

P = (-10 +/- 2*sqrt(25 + mG))/2m

P = (-5 +/- sqrt(25 + mG))/m

Answer 2

P=G or mp+10=g

solving mp+10=g you subtract 10 from each side giving you

mp=g-10

dividing each side by m you get

P=(g-10)/m

so i believe your two answers are P=G and P=(g-10)/m