Question

solve and check equation:

(x^2+16x+64)^3/4-12=15

Answer 1

x=-17, x=1

Answer 2

how did you get that?!

Answer 3

It's a quadratic equation. Set equal to zero. Solve by combining like terms.

Answer 4

If you need more information give me a second. lol

Answer 5

okay thanks ill wait :)

Answer 6

okay thanks ill wait :)

Answer 7

(x^(2)+16x+64)^((3)/(4))-12=15

Since -12 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 12 to both sides.
(x^(2)+16x+64)^((3)/(4))=12+15

Add 15 to 12 to get 27.
(x^(2)+16x+64)^((3)/(4))=27

Eliminate the fractional exponent on the lefthand side by raising both sides by to the (4)/(3) power.
((x^(2)+16x+64)^((3)/(4)))^((4)/(3))=(27)^((4)/(3))

Expand the exponent of (4)/(3) to each factor in the expression (x^(2)+16x+64)^((3)/(4)).
((x^(2)+16x+64))=(27)^((4)/(3))

Remove the parentheses from the numerator.
(x^(2)+16x+64)=(27)^((4)/(3))

Remove the parentheses around the expression x^(2)+16x+64.
x^(2)+16x+64=(27)^((4)/(3))

Expand the exponent ((4)/(3)) to the expression.
x^(2)+16x+64=(27^((4)/(3)))

An expression with a fractional exponent can be written as a radical with an index equal to the denominator of the exponent.
x^(2)+16x+64=((~3:(27))^(4))

Pull all perfect cube roots out from under the radical. In this case, remove the 3 because it is a perfect cube.
x^(2)+16x+64=((3)^(4))

Expand the exponent (4) to the expression.
x^(2)+16x+64=((3^(4)))

Raising a number to the 4th power is the same as multiplying the number by itself 4 times. In this case, 3 raised to the 4th power is 81.
x^(2)+16x+64=((81))

Remove the parentheses from the numerator.
x^(2)+16x+64=(81)

Remove the parentheses from the numerator.
x^(2)+16x+64=81

To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
x^(2)+16x-17=0

In this problem 17*-1=-17 and 17-1=16, so insert 17 as the right hand term of one factor and -1 as the right-hand term of the other factor.
(x+17)(x-1)=0

Set each of the factors of the left-hand side of the equation equal to 0.
x+17=0_x-1=0

Since 17 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 17 from both sides.
x=-17_x-1=0

Set each of the factors of the left-hand side of the equation equal to 0.
x=-17_x-1=0

Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides.
x=-17_x=1

The complete solution is the set of the individual solutions.
x=-17,1

Answer 8

too much? lol

Answer 9

thank you soo much but you could have just written it out! :p

Answer 10

haha, well it's important to understand whats confusing you. I have a program that generates everything if someone needs details. : )

I originally solved on paper, but thought a detailed answer might help you more!

Answer 11

aha yes thank you though!! i mean i had the basics i just didnt equal everything to 0 i would put 17 there instead or w.e

Answer 12

yeah, just remember, if you have something with x^2 in it and x then a constant (a number) there's a good chance you can use quadratics, or even the quadratic formula to solve it!