Question

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

Answer 1

Answer:

The final answers are:

$x = 4$

$x = -\frac{1}{2}$

Step-by-step explanation:

-The equation:

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

Use the Quadratic Formula:

$\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

$x =\frac{-(-7)\pm \sqrt{(-7)^2-4\time2(-4)} }{2\times2}$

-Then, you solve:

$x = \frac{-(-7)\pm \sqrt{(-7)^2-4\time2(-4)} }{2\times2}$

-Multiply -7 by the exponent 2:

$x =\frac{-(-7)\pm \sqrt{49-4\time2(-4)} }{2\times2}$

-Multiply to the 4 and the 2:

$x =\frac{-(-7)\pm \sqrt{49-8(-4)} }{2\times2}$

-Distribute -4 by 8:

$x=\frac{-(-7)\pm \sqrt{49+32} }{2\times2}$

-Add 49 and 32 together:

$x =\frac{-(-7)\pm \sqrt{81} }{2\times2}$

-Take the square root of 81:

$x= \frac{-(-7)\pm 9 }{2\times2}$

-The opposite of -7 is 7:

$x = \frac{7\pm 9 }{2\times2}$

-Multiply 2 times 2:

$x = \frac{7\pm 9 }{4}$

-Add both the 7 and 9:

$x = \frac{16}{4}$

-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:

$x = \frac{-2}{4}$

$x = -\frac{1}{2}$

So, the second answer is $x = -\frac{1}{2}$.

-The results are:

$x =4$

$x = -\frac{1}{2}$