Answer:
1).[tex](x+\frac{1}{4})^{2}=\frac{4}{9}[/tex]
2).[tex]x+\frac{1}{4}=\pm \frac{2}{3}[/tex]
Step-by-step explanation:
Here the given equation is [tex]x^{2}+\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}[/tex]
We have to factor the perfect square trinomial on the left side of the equation
So left side of the equation is [tex]x^{2}+\frac{1}{2}x+\frac{1}{16}[/tex]
= [tex]x^{2}+2\times \frac{1}{4}x+(\frac{1}{4})^{2}[/tex]
[tex]=(x+\frac{1}{4})^{2}[/tex] since [(a+b)²= a²+b²+2ab]
Therefore the factorial form of the equation will be
[tex](x+\frac{1}{4})^{2}=\frac{4}{9}[/tex]
Now we have to solve the equation by applying square root property
[tex]\sqrt{(x+\frac{1}{4})^{2}}=\sqrt{\frac{4}{9}}[/tex]
[tex]x+\frac{1}{4}=\pm \frac{2}{3}[/tex]
Answer:
1. Perfect square trinomial on left sides is [tex](x+\frac{1}{4})^2=\frac{4}{9}[/tex].
2. The equation after applying the square root property of equality is [tex]x+\frac{1}{4}=\pm \frac{2}{3}[/tex].
Step-by-step explanation:
The given equation is
[tex]x^2+\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}[/tex]
It can be written as
[tex]x^2+\frac{1}{2}x+(\frac{1}{4})^2=\frac{4}{9}[/tex]
Factor the perfect-square trinomial on the left side of the equation.
[tex]x^2+2(\frac{1}{4})x+(\frac{1}{4})^2=\frac{4}{9}[/tex]
[tex](x+\frac{1}{4})^2=\frac{4}{9}[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
Therefore the required equation is
[tex](x+\frac{1}{4})^2=\frac{4}{9}[/tex]
Taking square root both the sides.
[tex]\sqrt{(x+\frac{1}{4})^2}=\pm\sqrt{\frac{4}{9}}[/tex]
[tex]x+\frac{1}{4}=\pm \frac{2}{3}[/tex]
Therefore the equation after applying the square root property of equality is [tex]x+\frac{1}{4}=\pm \frac{2}{3}[/tex].
