Question

16x² -9 = 4ײ + (4x²+9)

Answer 1

For this case we must solve the following equation:

$16x ^ 2-9 = 4x ^ 2 + (4x ^ 2 + 9)$

We remove the parentheses on the right side:

$16x ^ 2-9 = 4x ^ 2 + 4x ^ 2 + 9$

We add similar terms on the right side:

$16x ^ 2-9 = 8x ^ 2 + 9$

We subtract $8x ^ 2$from both sides of the equation:

$16x ^ 2-8x ^ 2-9 = 9\\8x ^ 2-9 = 9$

We add 9 to both sides of the equation:

$8x ^ 2 = 9 + 9\\8x ^ 2 = 18$

We divide by 8 on both sides of the equation:

$x ^ 2 = \frac {18} {8}\\x ^ 2 = \frac {9} {4}$

We apply square root to both sides of the equation:

$x = \pm \sqrt {\frac {9} {4}}$

We have two roots:

$x_ {1} = \frac {3} {2}\\x_ {2} = - \frac {3} {2}$

Answer:

$x_ {1} = \frac {3} {2}\\x_ {2} = - \frac {3} {2}$