Can someone solve this by either factoring, graphing, quadratic formula, or completing the square? The problem is 3x^2+7x-24=13x

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Answer 1 · 2017-10-12T03:28:47

#x = 4 " "# and #" "x = -2#

First, subtract #13x# from both sides:

#3x^2 + 7x - 24 = 13x#

#3x^2 - 6x - 24 = 0#

Next, divide both sides by #3#

#x^2 - 2x - 8 = 0#

We need something of the form #x^2 + 2ax + a^2#.
Notice that our #2a# is #-2#, so we know #a = -1# and therefore #a^2 = 1#.

To get a perfect square, we can split #-8# into #+ 1 - 9#.

#x^2 - 2x + 1 - 9 = 0#

#(x^2 - 2x + 1) - 9 = 0#

#(x-1)^2 - 9 = 0#

Now, move the 9 to the other side, take the square root of both sides, and solve for #x#.

#(x-1)^2 = 9#

#x - 1 = +-3#

#x = 1+-3#

So now we have our two solutions; the only thing left to do is separate them:

#x = 1 + 3 " "# and #" "x = 1 - 3#

#x = 4 " "# and #" "x = -2#

Final Answer