Question

Im trying to figure out how to do this problem... I dont understand it, and would realy like to have someone show me how to do it... step by step. It is solve by completing the square- 4x^2-6x+5=0 any help would be greatly appreciated thanks.

Answer 1

\begin{align} 4 x^2 - 6 x + 5 =0 \end{align}
\begin{align} 4 x^2 - 6 x =-5 \end{align}

\begin{align} 4 (x^2 - \frac{6}{4} x) =-5 \end{align}
\begin{align} 4 (x^2 - \frac{3}{2} x) =-5 \end{align}

So far, what I did make sense

when we complete square , we half the term with 'x' and then square it
\[-3/2 * 1/2=(3/4)^2\]---> 9/16
\begin{align} 4 (x^2 - \frac{3}{2} x+\frac{9}{16}) =-5 \end{align}

add the same to other side
\begin{align} 4 (x^2 - \frac{3}{2} x+\frac{9}{16}) =-5+4\frac{19}{6} \end{align}

\begin{align} 4 (x - \frac{3}{4} )^2 =-5+4\frac{19}{6} \end{align}

Answer 2

Does that all say math processing error to anyone else?

Answer 3

Looks legal to me

Answer 4

Well then. Carry on.

Answer 5

Are you concerned about the (4) (19/6)??

Answer 6

I sure as hell am... isnt it supposed to be (9/16)??

Answer 7

and arent you suppoosed to add the -5+4... so the answer would be -1(9/16)??

Answer 8

Let me rewrite last two line

Answer 9

Now just clean it up

Answer 10

that is 4*(9/16)

Answer 11

\begin{align} 4 (x^2 - \frac{3}{2} x+\frac{9}{16}) =-5+4*\frac{9}{16} \end{align}

\begin{align} 4 (x - \frac{3}{4} )^2 =-5+4*\frac{9}{16} \end{align}

Answer 12

@bast0573 Pay particular to the 4 which is outside the paren on the left it applies to the 9/16 also and that is why it appears on the right.

Answer 13

What you add to the left you add to the right.

Answer 14

ok... so you would actually do the equationto solve it out?? which would come out to -5+(36/64)?