Answer:
The solutions to the quadratic equation using the quadratic formula will be:
[tex]x=\frac{1}{2},\:x=\frac{1}{4}[/tex]
Step-by-step explanation:
Given the equation
[tex]8x^2-6x+1=0[/tex]
solving with the quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=8,\:b=-6,\:c=1[/tex]
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}}{2\cdot \:8}[/tex]
as
[tex]\sqrt{\left(-6\right)^2-4\cdot \:8\cdot \:1}=2[/tex]
so
[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:2}{2\cdot \:8}[/tex]
Separating the solution
[tex]x_1=\frac{-\left(-6\right)+2}{2\cdot \:8},\:x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}[/tex]
solving
[tex]x_1=\frac{-\left(-6\right)+2}{2\cdot \:\:8}[/tex]
[tex]=\frac{6+2}{2\cdot \:8}[/tex]
[tex]=\frac{8}{16}[/tex]
[tex]=\frac{1}{2}[/tex]
and
[tex]x_2=\frac{-\left(-6\right)-2}{2\cdot \:8}[/tex]
[tex]=\frac{6-2}{2\cdot \:\:\:8}[/tex]
[tex]=\frac{4}{16}[/tex]
[tex]=\frac{1}{4}[/tex]
Therefore, the solutions to the quadratic equation using the quadratic formula will be:
[tex]x=\frac{1}{2},\:x=\frac{1}{4}[/tex]
