# Math Help - Equation to solve, anyone?

1. ## Equation to solve, anyone?

Solve the equation 5x - ||v|| v = ||w||(w-5x) for x with v = (1, 2, -4, 0) and w = (-3, 5, 1, 1 )

2. ## Re: Equation to solve, anyone?

so you have $||v|| = \sqrt{1^2 + 2^2 + 4^2 + 0^2} = \sqrt{21}$ and $||w|| = \sqrt{9 + 25 + 1 + 1} = \sqrt{36} = 6$
$5x - \sqrt{21}v = 6w - 30x$ [
$35x = 6w + \sqrt{21} v$
right side equals $\begin{bmatrix}-18 + \sqrt{21} \\ 30 + 2 * \sqrt{21} \\ 6 - 4*\sqrt{21} \\ 6 \end{bmatrix}$
multiply the right side by $\frac{1}{35}$
x = $\frac{1}{35} \begin{bmatrix}-18 + \sqrt{21} \\ 30 + 2 * \sqrt{21} \\ 6 - 4*\sqrt{21} \\ 6 \end{bmatrix}$