Question

Square Root

Answer 1

Answer:

1. Perfect square trinomial on left sides is $(x+\frac{1}{4})^2=\frac{4}{9}$.

2. The equation after applying the square root property of equality is $x+\frac{1}{4}=\pm \frac{2}{3}$.

Step-by-step explanation:

The given equation is

$x^2+\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}$

It can be written as

$x^2+\frac{1}{2}x+(\frac{1}{4})^2=\frac{4}{9}$

Factor the perfect-square trinomial on the left side of the equation.

$x^2+2(\frac{1}{4})x+(\frac{1}{4})^2=\frac{4}{9}$

$(x+\frac{1}{4})^2=\frac{4}{9}$        $[\because (a+b)^2=a^2+2ab+b^2]$

Therefore the required equation is

$(x+\frac{1}{4})^2=\frac{4}{9}$

Taking square root both the sides.

$\sqrt{(x+\frac{1}{4})^2}=\pm\sqrt{\frac{4}{9}}$

$x+\frac{1}{4}=\pm \frac{2}{3}$

Therefore the equation after applying the square root property of equality is $x+\frac{1}{4}=\pm \frac{2}{3}$.

Answer 2

Answer:

1).$(x+\frac{1}{4})^{2}=\frac{4}{9}$

2).$x+\frac{1}{4}=\pm \frac{2}{3}$

Step-by-step explanation:

Here the given equation is $x^{2}+\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}$

We have to factor the perfect square trinomial on the left side of the equation

So left side of the equation is $x^{2}+\frac{1}{2}x+\frac{1}{16}$

= $x^{2}+2\times \frac{1}{4}x+(\frac{1}{4})^{2}$

$=(x+\frac{1}{4})^{2}$    since [(a+b)²= a²+b²+2ab]

Therefore the factorial form of the equation will be

$(x+\frac{1}{4})^{2}=\frac{4}{9}$

Now we have to solve the equation by applying square root property

$\sqrt{(x+\frac{1}{4})^{2}}=\sqrt{\frac{4}{9}}$

$x+\frac{1}{4}=\pm \frac{2}{3}$