Answer:
The smallest solution is x=-1
Step-by-step explanation:
Quadratic Equation
We have:
[tex]f(x)=2x+1[/tex]
[tex]g(x)=-(x-1)^2+3[/tex]
We'll find the solutions of f(x)=g(x), or:
[tex]2x+1=-(x-1)^2+3[/tex]
Operating:
[tex]2x+1=-(x^2-2x+1)+3[/tex]
[tex]2x+1=-x^2+2x-1+3[/tex]
Rearranging all terms on the left side:
[tex]2x+1+x^2-2x+1-3=0[/tex]
Simplifying:
[tex]x^2-1=0[/tex]
Since the term with the x is missing, we can solve for x:
[tex]x^2=1\qquad\Rightarrow x=\sqrt{1}=\pm 1[/tex]
There are two solutions:
x=1, x=-1
The smallest solution is x=-1
