Answer:
The values of x are [tex]x= 1+\frac{1+\sqrt10}{2} \,\,and \,\, x= 1-\frac{1+\sqrt10}{2}[/tex]
Step-by-step explanation:
The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Our equation is:
[tex]2x^2 = 4x -7\\2x^2-4x+7=0[/tex]
a= 2, b= -4 and c =7
Putting the values in quadratic formula:
[tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4(2)(7)}}{2(2)}\\x=\frac{4\pm\sqrt{16-56}}{4}\\x=\frac{4\pm\sqrt{-40}}{4}[/tex]
Since we have -40 in the under root we will find its factors and simplify:
Factors of 40 = 2*2*2*5
[tex]x=\frac{4\pm\sqrt{2*2*2*5}}{4}\\x=\frac{4\pm\sqrt{2^2 *2*5}}{4}\\x=\frac{4\pm\sqrt{2^2}\sqrt{2*5}}{4}\\x=\frac{4\pm2\sqrt{10}}{4}\\x=\frac{4+2\sqrt{10}}{4} \,\, and \,\, x=\frac{4-2\sqrt{10}}{4}[/tex]
The values of x are:
[tex]x=\frac{4+2\sqrt{10}}{4} \,\, and \,\, x=\frac{4-2\sqrt{10}}{4}[/tex]
[tex]x= \frac{4}{4}+ \frac{2+\sqrt10}{4} \,\,and \,\, x= \frac{4}{4}- \frac{2+\sqrt10}{4}\\x= 1+\frac{1+\sqrt10}{2} \,\,and \,\, x= 1-\frac{1+\sqrt10}{2}[/tex]
