Answer:
[tex]x=\displaystyle\frac{5+\sqrt{21}}{2}[/tex] or [tex]x=\displaystyle\frac{5-\sqrt{21}}{2}[/tex]
Step-by-step explanation:
Hi there!
[tex](x+1)^2=7x[/tex]
Expand the parentheses:
[tex]x^2+2x+1=7x[/tex]
Move 7x to the other side:
[tex]x^2+2x-7x+1=0\\x^2-5x+1=0[/tex]
Apply the quadratic formula:
[tex]x=\displaystyle\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] where [tex]ax^2+bx+c=0[/tex]
Plug in the values a, b and c:
[tex]x=\displaystyle\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(1)}}{2(1)}\\\\x=\displaystyle\frac{5\pm\sqrt{25-4}}{2}\\\\x=\displaystyle\frac{5\pm\sqrt{21}}{2}[/tex]
I hope this helps!
