Answer:
The final answers are:
[tex]x = 4[/tex]
[tex]x = -\frac{1}{2}[/tex]
Step-by-step explanation:
-The equation:
[tex]2x^2 -7x-4=0[/tex]
Use the Quadratic Formula:
[tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x =\frac{-(-7)\pm \sqrt{(-7)^2-4\time2(-4)} }{2\times2}[/tex]
-Then, you solve:
[tex]x = \frac{-(-7)\pm \sqrt{(-7)^2-4\time2(-4)} }{2\times2}[/tex]
-Multiply -7 by the exponent 2:
[tex]x =\frac{-(-7)\pm \sqrt{49-4\time2(-4)} }{2\times2}[/tex]
-Multiply to the 4 and the 2:
[tex]x =\frac{-(-7)\pm \sqrt{49-8(-4)} }{2\times2}[/tex]
-Distribute -4 by 8:
[tex]x=\frac{-(-7)\pm \sqrt{49+32} }{2\times2}[/tex]
-Add 49 and 32 together:
[tex]x =\frac{-(-7)\pm \sqrt{81} }{2\times2}[/tex]
-Take the square root of 81:
[tex]x= \frac{-(-7)\pm 9 }{2\times2}[/tex]
-The opposite of -7 is 7:
[tex]x = \frac{7\pm 9 }{2\times2}[/tex]
-Multiply 2 times 2:
[tex]x = \frac{7\pm 9 }{4}[/tex]
-Add both the 7 and 9:
[tex]x = \frac{16}{4}[/tex]
-Divide 16 by 4 to get 4:
[tex]x = 4[/tex]
So, the first answer [tex]x = 4[/tex] 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:
[tex]x = \frac{-2}{4}[/tex]
[tex]x = -\frac{1}{2}[/tex]
So, the second answer is [tex]x = -\frac{1}{2}[/tex].
-The results are:
[tex]x =4[/tex]
[tex]x = -\frac{1}{2}[/tex]
