Answer:
x = 0.417 or x = -0.917
Step-by-step explanation:
We are given the following expression and we are to solve it for the variable x:
[tex] x ^2 + \frac { 1 } { 2 } x + \frac { 1 } { 1 6 } = \frac { 4 } { 9 } [/tex]
We will find the least common multiple of 2. 6 and 9:
[tex]x^2 \times 144 +\frac{1}{2}x \times 144 +\frac{1}{16} \times 144 = \frac{4}{9} \times 144[/tex]
Simplifying it to get:
[tex]144x^2+72x+9=64[/tex]
[tex]144x^2+72x+9-64=0[/tex]
[tex]144x^2+72x-55=0[/tex]
Using the quadratic formula to solve for x:
[tex]x=\frac{-b \pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-72 \pm\sqrt{72^2-4(144)(-55)} }{2a}[/tex]
[tex]x=\frac{5}{12}[/tex] or [tex]0.417[/tex]
[tex]x=-\frac{11}{12}[/tex] or [tex]-0.917[/tex]
