Question

Solve for x: - 15a²x² - 16abx - 15b² = 0

Answer 1

Factor with quadratic formula.

In general, given $\rm a{x}^{2}+bx+c$ the factored form is:

$\\ \rm a \bigg(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a} \bigg) \bigg(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a} \bigg)$

In this case, $\rm a=15{x}^{2}$ b=-16bx and $\rm c=-15{b}^{2}$

$\\ \tt15{x}^{2} \bigg(a-\frac{16bx+\sqrt{{(-16bx)}^{2}-4\times 15{x}^{2}\times -15{b}^{2}}}{2\times 15{x}^{2}} \bigg) \bigg(a-\frac{16bx-\sqrt{{(-16bx)}^{2}-4\times 15{x}^{2}\times -15{b}^{2}}}{2\times 15{x}^{2}} \bigg)</p><p></p><p>$

Simplify.

• (3xa−5b)(5xa+3b)=0

When 3xa−5b=0 or 5xa+3b=0

Solve each of the 2 equations above.

$\\ \rm\dashrightarrow x=\frac{5b}{3a},-\frac{3b}{5a}$