Question

Which is a solution to the equation?

(x − 3)(x − 5) = 35

x = −8
x = −5
x = 2
x = 10

Answer 1

10 on exam

Explanation:

Answer 2

-The solutions are:

`x = 10`

`x = -2`

Explanation:

-Solve the equation:

`(x-3)(x-5) =35`

-Use Distributive property to multiply the
`x -3` by
`x -5` and combine like terms:

`(x-3)(x-5) =35`

`x^2-8x + 15 = 35`

-Subtract 35 from 15:

`x^2 - 8x + 15 -35 = 35 -35`

`x^2 - 8x - 20 =0`

-Use the quadratic formula and substitute 1 for
`a`, -8 for
`b` , and -20 for
`c` :

`(-b\pm√(b^2-4ac) )/(2a)`

`(-(-8)\pm√((-8)^2-4(-20)) )/(2)`

-Simplify the 8 by the exponent 2:

`x = (-(-8)\pm√((-8)^2-4(-20)) )/(2)`

`x = (-(-8)\pm√(64-4(-20)) )/(2)`

-Multiply -20 by -4:

`x = (-(-8)\pm√(64-4(-20)) )/(2)`

`x = (-(-8)\pm√(64+80) )/(2)`

-Add both 64 and 80 together:

`x = (-(-8)\pm√(64+80) )/(2)`

`x = (-(-8)\pm√(144) )/(2)`

-Take the square root of 144:

`x = (-(-8)\pm√(144) )/(2)`

`x = (-(-8)\pm 12 )/(2)`

-Change -8 to 8 , because negative and negative equals a positive:

`x = (-(-8)\pm 12 )/(2)`

`x =(8\pm 12 )/(2)`

-Solve the equation when
`\pm` is in addition. So, you would add 8 and 12 together:

`x =(8\pm 12 )/(2)`

`x =(8 + 12 )/(2)`

`x =(20 )/(2)`

-Divide 20 by 2:

`x =(20)/(2)`

`x = 10`

So, the first answer is
`x = 10`.

-To find the second answer, you need to solve the equation when
`\pm` is in subtraction. So, you would subtract both 8 and 12 together:

`x =(8\pm 12 )/(2)`

`x =(8 - 12 )/(2)`

`x = (-4)/(2)`

-Divide -4 by 2:

`x = (-4)/(2)`

`x = -2`

So, the second answer is
`x = -2` .

The solutions are:

`x = 10`

`x = -2`