Question

Im in algebra 1 and I need help trying to find the answer to “p=√4p +5”.

Answer 1

Answer and Step-by-step explanation:

We are trying to solve for p in the equation p =
`√(4p)` + 5.

First, subtract the 5 from both sides of the equation.

p - 5 =
`√(4p)` + 5 - 5

p - 5 =
`√(4p)`

Second, to make things easier for ourselves, we need to square both sides of the equation to get rid of the square root.

`(p-5)^2` =
`(√(4p))^2`

`p^2 - 10p + 25 = 4p`

Now, subtract 4p from both sides of the equation.

`p^2 - 10p + 25 - 4p = 4p - 4p`

`p^2 - 14p + 25 = 0`

Now, we plug these values into the Quadratic Equation formula,

The Quadratic Equation formula is as follows:
`x=(-b\pm√(b^2-4ac) )/(2a)`

Where:

x will equal p

a will equal the coefficient of the first term of the equation (the first term is
`p^(2)` and the coefficient is 1)

b will equal the coefficient of the second term of the equation (the second term is -10p and the coefficient is -10)

c will equal the coefficient of the third term of the equation (the third term is 25 and the coefficient is 25)

Plug all the terms into the quadratic equation.

`p = (-(-14) \pm√((-14)^2-4(1)(25)) )/(2(1)) \\\\p = 7+√(196-100)/2 , 7-√(196-100) /2\\\\p = 7 + √(96)/2 ,7-√(96) /2\\\\\\p=7+2√(6) ,7-2√(6)`

So, the answer is both:

`p=7+2√(6) ,7-2√(6)`.

Have a good day!