Respuesta :
Answer:
[tex]x_{1}=\frac{1}{2}\\x_{2}=-\frac{1}{4}[/tex]
Step-by-step explanation:
Hello
For ax2 + bx + c = 0,the values of x which are the solutions of the equation are given by
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
± means there are two solution for x, X1 and X2
[tex]x_{1} =\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\x_{2} =\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
Step 1
convert 8x2-2x=1 into the form ax2 + bx + c = 0 ( right side equal to cero)
subtract 1 in each side
[tex]8x^{2} -2x=1\\8x^{2} -2x-1=1-1\\8x^{2} -2x-1=0[/tex]
Step 2
replace in the equation
Let
a=8
b=-2
c=-1
Hence
[tex]x_{1} =\frac{-b+\sqrt{b^{2}-4ac }}{2a}\\ x_{1}=\frac{-(-2)+\sqrt{(-2)^{2}-4(8)(-1) } }{2*8}\\x_{1} =\frac{+2+\sqrt{4+32 }}{16}\\x_{1} =\frac{+2+\sqrt{36 } }{16}\\x_{1} =\frac{2+\sqrt{36 }}{16}\\x_{1} =\frac{2+6}{16} \\x_{1} =\frac{8}{16} \\x_{1}=-\frac{1}{2}[/tex]
Now, X2
[tex]x_{2} =\frac{-b-\sqrt{b^{2}-4ac }}{2a}\\ x_{2}=\frac{-(-2)-\sqrt{(-2)^{2}-4(8)(-1) } }{2*8}\\x_{1} =\frac{+2-\sqrt{4+32 }}{16}\\x_{2} =\frac{+2-\sqrt{36 } }{16}\\x_{2} =\frac{2-\sqrt{36 }}{16}\\x_{2} =\frac{2-6}{16} \\x_{2} =\frac{-4}{16} \\x_{2}=-\frac{1}{4}[/tex]
Have a great day
