Respuesta :
Answer
[tex]x=\frac{-11+5\sqrt{5} }{2} ,x=\frac{-11-5\sqrt{5} }{2}[/tex]
Explanation
Let's solve our quadratic equation step by step.
Step 1. Subtract [tex]\frac{125}{4}[/tex] from both sides
[tex]x^2+11x+\frac{121}{4}= \frac{125}{4}[/tex]
[tex]x^2+11x+\frac{121}{4}-\frac{125}{4}= \frac{125}{4}-\frac{125}{4}[/tex]
[tex]x^2+11x-1=0[/tex]
Step 2. Complete the square
Using the formula for completing the square:
[tex]x+bx+c=(x-h)^2+k[/tex]
where
[tex]h=\frac{-b}{2}[/tex]
[tex]k=c-\frac{b^2}{4}[/tex]
We can infer from [tex]x^2+11x-1=0[/tex] that [tex]b=11[/tex] and [tex]c=-1[/tex], so let's find [tex]h[/tex] and [tex]k[/tex]:
[tex]h=\frac{-b}{2}[/tex]
[tex]h=\frac{-11}{2}[/tex]
[tex]k=-1-\frac{11^2}{4}[/tex]
[tex]k=-1-\frac{121}{4}[/tex]
[tex]k=-\frac{125}{4}[/tex]
Now we can replace the values in our formula:
[tex]x+bx+x=(x-h)^2+k[/tex]
[tex]x^2+11x-1=(x-(-\frac{11}{2} ))^2+(-\frac{125}{4} )[/tex]
[tex]x^2+11x-1=(x+\frac{11}{2} )^2-\frac{125}{4}[/tex]
[tex](x+\frac{11}{2} )^2-\frac{125}{4}=0[/tex]
Step 3. Add [tex]\frac{125}{4}[/tex] to both sides
[tex](x+\frac{11}{2} )^2-\frac{125}{4}+\frac{125}{4}=0+\frac{125}{4}[/tex]
[tex](x+\frac{11}{2} )^2=\frac{125}{4}[/tex]
Step 4. Take square root to both sides
[tex]x+\frac{11}{2} =+or-\sqrt{\frac{125}{4} }[/tex]
[tex]x+\frac{11}{2}=+or-\frac{5\sqrt{5} }{2}[/tex]
Step 5. Subtract [tex]\frac{11}{2}[/tex] form both sides
[tex]x+\frac{11}{2}-\frac{11}{2} =+or-\frac{5\sqrt{5} }{2}-\frac{11}{2}[/tex]
[tex]x =+or-\frac{5\sqrt{5} }{2}-\frac{11}{2}[/tex]
Solutions of the equation:
[tex]x=\frac{-11+5\sqrt{5} }{2} ,x=\frac{-11-5\sqrt{5} }{2}[/tex]
Answer:
Step-by-step explanation:
ANSWER :) x=-11/2+5 Sq root 5/2
(D) on edge
