Question

Solve 2x^2- 7x - 4 = 0 using the Quadratic Formula.

Answer 1

The final answers are:

`x = 4`

`x = -(1)/(2)`

Explanation:

-The equation:

`2x^2 -7x-4=0`

Use the Quadratic Formula:

`(-b\pm√(b^2-4ac) )/(2a)`

`x =(-(-7)\pm √((-7)^2-4\time2(-4)) )/(2*2)`

-Then, you solve:

`x = (-(-7)\pm √((-7)^2-4\time2(-4)) )/(2*2)`

-Multiply -7 by the exponent 2:

`x =(-(-7)\pm √(49-4\time2(-4)) )/(2*2)`

-Multiply to the 4 and the 2:

`x =(-(-7)\pm √(49-8(-4)) )/(2*2)`

-Distribute -4 by 8:

`x=(-(-7)\pm √(49+32) )/(2*2)`

-Add 49 and 32 together:

`x =(-(-7)\pm √(81) )/(2*2)`

-Take the square root of 81:

`x= (-(-7)\pm 9 )/(2*2)`

-The opposite of -7 is 7:

`x = (7\pm 9 )/(2*2)`

-Multiply 2 times 2:

`x = (7\pm 9 )/(4)`

-Add both the 7 and 9:

`x = (16)/(4)`

-Divide 16 by 4 to get 4:

`x = 4`

So, the first answer
`x = 4` and you need to find the second answer.

-To find the second answer, you to reduce the fraction to lowest terms and canceling out the 2:

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

`x = -(1)/(2)`

So, the second answer is
`x = -(1)/(2)`.

-The results are:

`x =4`

`x = -(1)/(2)`