Question

x is a number such that x2+3x+9=0. What is the value of x3?

Answer 1

All the numbers next to x are squared

Answer 2

Quadritic equation

Answer 3

The Equation button is really pretty easy to use...try it!

Answer 4

Do you know how to find x in that equation?

Answer 5

\[x ^{ 2}+3x+9=0\]

Answer 6

Nopet"

Answer 7

Okay, we've got a couple of options: factoring, completing the square, and quadratic formula.

For factoring this work, we would need to find two factors of 9 that sum to 3. That ain't happenin' :-)

Completing the square:
Make sure you have your leading coefficient = 1 (divide through by it, if necessary), and move the numeric term to the other side of the equals sign:
\[x^2+3x = -9\]Now take half of the coefficient of the x term, square it, and add that quantity to both sides:
\[x^2+3x+(\frac{3}{2})^2 = -9 + (\frac{3}{2})^2\]Now write the left hand side as a square:
\[(x+\frac{3}{2})^2 = -9 + \frac{9}{4} = -\frac{27}{4}\]Take the square root of both sides
\[x+\frac{3}{2} =\pm i\frac{3\sqrt{3}}{2}\]
\[x = -\frac{3\pm i3\sqrt{3}}{2} = -\frac{3}{2}(1\pm i\sqrt{3})\]

Answer 8

With the quadratic formula, the square is already completed for us :)
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a},ax^2+bx+c=0,a\ne0\]
I'll let you convince yourself that the same result is obtained.

Answer 9

Now to find \(x^3\), you need to sharpen your pencil and find the value of \[(-\frac{3}{2}(1\pm i\sqrt{3}))(-\frac{3}{2}(1\pm i\sqrt{3}))(-\frac{3}{2}(1\pm i\sqrt{3}))\]You can use either + or - (use the same one for all three!) as the result will be the same. I would probably set aside the -3/2 and just do \((1-i\sqrt{3})^3\) first, then multiply by \((-3/2)^3\). One of my favorite tactics is to eliminate radicals while doing algebra by replacing them with a letter, then substituting back later. I would do \((1-ia)(1-ia)(1-ia)\) and when the dust settles, replace \(a\) with \(\sqrt{3}\) and do any further simplification that is possible.

Answer 10

okay sorry i was do something at the time

Answer 11

\[x^{3}\]

Answer 12

for x3 i mean

Answer 13

oay guide me steo by step not this

Answer 14

\[(1-ia)(1-ia) = \]?

Answer 15

@Rancd You still there?