If $m = 6x + 5$, what equation is equivalent to $(6x + 5)^2 - 10=-18x - 15$ in terms of $m$?
This question I am asking right now comes from the Khan Academy practice task entitled 'Solve quadratic equations by using structure', so the credit goes to them.
So, if $m = 6x + 5$, then what equation is equivalent to $(6x + 5)^2 - 10 = -18x - 15$ in terms of $m$? I have been thumping my head on this, but it just doesn't seem to get me anywhere. Can anyone help me? Until then, I'll be attempting to solve the problem and look for answers.
By the way, the answer is supposed to be in the form of: $$ax^2 + bx + c = 0$$
$\endgroup$ 12 Answers
$\begingroup$The goal is to replace all the $x$'s with $m$'s.
This equation is quite convenient as it is for replacement. As @ASKASK noted in his answer, the right side can be rewritten as $-3m$.
The left side falls exactly as you would expect it to. Because $m = 6x + 5$, you can just rewrite the left side as $m^2-10$. (Note: $(6x-5)^2 = m^2$).
At this point, you should have an equation with $m$'s on both sides. You'll probably want to rearrange and factor it to solve for $m$.
But that's another question.
$\endgroup$ 8 $\begingroup$Hint: $$-18x-15=-3(6x+5)=-3m$$
$\endgroup$ 6
