Question

I need help with solving equations...

Answer 1

\[y=-2x^2\]\[5x^2+y^2=44\]

Answer 2

Focus on the second equation. Replace every copy of 'y' with -2x^2
\[\Large 5x^2 + y^2 = 44\]
\[\Large 5x^2 + \left(y\right)^2 = 44\]
\[\Large 5x^2 + \left(-2x^2\right)^2 = 44\]
\[\Large 5x^2 + 4x^4 = 44\]
What comes next?

Answer 3

thats the part that im having troubles with, i cant combine the x's but do I devide to get rid of the 5 and 4?

Answer 4

Get everything to one side
\[\Large 5x^2 + 4x^4 = 44\]
\[\Large 5x^2 + 4x^4-44 = 44-44\]
\[\Large 4x^4+5x^2-44 = 0\]

Answer 5

If we let z = x^2, then z^2 = x^4 after squaring both sides

we can replace the x^4 with z^2
we can replace the x^2 with z

to go from this
\[\Large 4x^4+5x^2-44 = 0\]
to this
\[\Large 4z^2+5z-44 = 0\]

Answer 6

okay

Answer 7

then do i complete the square?

Answer 8

or use the quadratic formula

Answer 9

so i got to \[-130.288\times i\]

Answer 10

over 8

Answer 11

that's incorrect

Answer 12

and that ends up \[-16.286 \times i\]

Answer 13

yeah...

Answer 14

is right?