Question

Solve x^2 + 1/2x + 1/16 = 4/9

Answer 1

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

Answer 2

Answer:

$x=\frac{5}{12}\text{ or }x=-\frac{11}{12}$

Step-by-step explanation:

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

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

$(x)^2+2\times x\times \frac{1}{4}+(\frac{1}{4})^2=(\frac{2}{3})^2$

$(x+\frac{1}{4})^2=(\frac{2}{3})^2$  $(\because (x+y)^2=x^2+2xy+y^2)$

$x+\frac{1}{4}=\pm \sqrt{(\frac{2}{3})^2}$

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

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

$x=-\frac{1}{4}+ \frac{2}{3}\text{ or }x=-\frac{1}{4}-\frac{2}{3}$

$\implies x=\frac{5}{12}\text{ or }x=-\frac{11}{12}$