For this case we must solve the following equation:
[tex]16x ^ 2-9 = 4x ^ 2 + (4x ^ 2 + 9)[/tex]
We remove the parentheses on the right side:
[tex]16x ^ 2-9 = 4x ^ 2 + 4x ^ 2 + 9[/tex]
We add similar terms on the right side:
[tex]16x ^ 2-9 = 8x ^ 2 + 9[/tex]
We subtract [tex]8x ^ 2[/tex]from both sides of the equation:
[tex]16x ^ 2-8x ^ 2-9 = 9\\8x ^ 2-9 = 9[/tex]
We add 9 to both sides of the equation:
[tex]8x ^ 2 = 9 + 9\\8x ^ 2 = 18[/tex]
We divide by 8 on both sides of the equation:
[tex]x ^ 2 = \frac {18} {8}\\x ^ 2 = \frac {9} {4}[/tex]
We apply square root to both sides of the equation:
[tex]x = \pm \sqrt {\frac {9} {4}}[/tex]
We have two roots:
[tex]x_ {1} = \frac {3} {2}\\x_ {2} = - \frac {3} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {3} {2}\\x_ {2} = - \frac {3} {2}[/tex]
