Question

How do you solve `7(t^2+5t-9)+t=t(7t-2)+13`?

Answer 1

`t=2`

Explanation:

`"the first step is to distribute the brackets on both sides"`

`rArr7t^2+35t-63+t=7t^2-2t+13`

`7t^2+36t-63=7t^2-2t+13larr" simplify left side"`

`"collect variables on left and numeric values on right"`

`cancel(7t^2)cancel(-7t^2)+36t+2t=13+63`

`rArr38t=76`

`"divide both sides by 38"`

`(cancel(38)color(white)(x)t)/cancel(38)=76/38`

`rArrt=2`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides equate then it is the solution.

`"left "=7(4+10-9)+2=(7xx5)+2=37`

`"right "=2(14-2)+13=(2xx12)+13=37`

`rArrt=2" is the solution"`