# Math Help - Passage of a norm of a vector exercise

1. ## Passage of a norm of a vector exercise

Hi,

I've an example of vector exercise that achieved the following step onwards to resolving. |vector r| is the norm of the vector.

|vector r|^2 = 100(25t^2-14t+2) = 100((5t-(14/10)^2) - (14/10)^2 +2)

I don't understand how the passage is made, because for me the values inside the parameter of the first count is a quadratic function who has the consequent result:
t=(-14+/-squarert(-4))/50.

Can anybody explain me how the passage of the |vector r|^2 is made?

Thanks,
Pedro

2. Hi Pedro

$(5t-\frac{14}{10})^2\;=\;25t^2-14t+(\frac{14}{10})^2$

Therefore
$25t^2-14t+2\;=\;(5t-\frac{14}{10})^2-(\frac{14}{10})^2+2$

3. Originally Posted by pedrosacosta
Hi,

I've an example of vector exercise that achieved the following step onwards to resolving. |vector r| is the norm of the vector.

|vector r|^2 = 100(25t^2-14t+2) = 100((5t-(14/10))^2 - (14/10)^2 +2)

I don't understand how the passage is made, because for me the values inside the parameter of the first count is a quadratic function who has the consequent result:
t=(-14+/-squarert(-4))/50.

Can anybody explain me how the passage of the |vector r|^2 is made?

Thanks,
Pedro
You've made an insidious typo: See the correction in red.

Here is nothing done but completing the square:

$|\vec r|^2=100(25t^2-14t+2)=100((5t)^2-14t+\left(\frac{14}{10}\right)^2 - \left(\frac{14}{10}\right)^2+2) =$ $100\left(\left(5t-\left(\frac{14}{10}\right)\right)^2-\left(\frac{14}{10}\right)^2+2\right)$

You only have to translate the ^2 behind the closing paranthese.