Question

Solve 3t^2 – 4t = –30 by completing the square.

Answer 1

Divide by 3 to both sides.

Answer 2

When you complete the square, the t^2 must be monic and without a coefficient.

Answer 3

wait, im still confused haha

Answer 4

Divide both sides by 3, so that it becomes \[t^2 -(\frac{4}{3}t = -10\]Completing the square relies on the first term having a coefficient of 1.

Answer 5

@#$#@$
\[t^2-(\frac{4}{3})t - 10\]

Answer 6

I'm actually not sure how to do it the "completing the square" way but you can do it like this:
\[3t^{2}-4t=-30 \leftrightarrow 3t^{2}-4t -30=0\]
Then you can solve for t like this:
\[t=\frac{ 4 \pm\sqrt{-4^{2}-4*3*-30} }{ 2*3 }\]
That is the quadratic formula, and it works like this:
\[x=\frac{ -b \pm \sqrt{b^2-4ac}}{ 2a }\]
Where a, b and c is placed like this in the equation:
\[ax^2bx+c=0\]

Answer 7

You can watch a nice video on it here ;)
http://www.youtube.com/watch?v=i7idZfS8t8w

Answer 8

@memand That's just fluffing around. You're not getting to the point that you must complete the square. That's not completing the square. Simple as that. When the question asks you to complete the square, you complete the square. That's when people who just invent stuff from mid-air will always get 0 marks.

Answer 9

\[t^2 - (\frac{4}{3})t = -10\]
You want the variable terms on the left hand side, and the numeric term on the right hand side. Now, you take half of the coefficient of the t term, square it, and add it to both sides.

\[t^2 -(\frac{4}{3})t + (\frac{4}{3}*\frac{1}{2})^2 = -10 + (\frac{4}{3}*\frac{1}{2})^2\]
\[t^2 -(\frac{4}{3})t + \frac{4}{9} = -10 + \frac{4}{9}\]Write the left hand side as a square
\[(t-\frac{2}{3})^2 = -\frac{86}{9}\]Now you can take the square root of both sides\[(t-\frac{2}{3})= \pm\sqrt{-\frac{86}{9}} = \pm\frac{i \sqrt{86}}{3}\]so \[t = \frac{2\pm i\sqrt{86}}{3}\]

Answer 10

oh okay, that makes sense :) thankyou whpalmer4 !

Answer 11

Kind of a messy problem to illustrate completing the square. Here's a better one:

\[2x^2 = 4x + 30\]First put it in the required form, with x on left and numbers on right
\[2x^2-4x=30\]Now divide both sides by 2 to get the coefficient of x^2 to 1
\[x^2 - 2x = 15\]Take half the value of the x coefficient, square it, and add to both sides
\[x^2 - 2x + (1)^2 = 15 + (1)^2\]Write as a square
\[(x-1)^2 = 16\]Square root of both sides gives
\[(x-1) = \pm 4\]Solve for x
\[x = 1\pm 4\]

Answer 12

@Azteck Just to prove that I didn't pull that out of my imagination, please watch this vide and realize that you will get exactly the same result...
http://www.youtube.com/watch?v=r3SEkdtpobo

Answer 13

@memand Sorry but it doesn't look like you understand what I said above. You're not mean to use different methods to solve this question when the question specifically says to use completing the square. Dang mate, you need understand that reading the question is one of the main steps that people find it hard to do.

Answer 14

you're not meant*

Answer 15

Ok :)

Answer 16

@memand As a learning exercise and penance for suggesting the OP solve the problem in a different way than requested, complete the square on ax^2 + bx + c = 0 to derive the quadratic formula...

Answer 17

@whpalmer4 That is the best ways to understand completing the square. That is probably one of the first things that students do in class in order to understand completing the square and how the quadratic formula can be derived using completing the square.

Answer 18

@whpalmer4 Yeah, that's not gonna happen until tomorrow morning since it's 3:44 in the morning where I'm at. But I might do it tomorrow morning, just because ;)

Answer 19

Tomorrow morning = when I wake up...