Question

How do you solve `sqrt(2v-7)=v-3`?

Answer 1

`v=+4`

Explanation:

Roots make life a bit more difficult so lets get rid of it!

Square both sides

`2v-7=(v-3)^2`

`2v-7=(v-3)(v-3)` ......................Equation(1)
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Consider `color(blue)((v-3))color(brown)((v-3))`

Multiply everything in the right hand bracket by everything in the left hand bracket.

`color(brown)(color(blue)(v)(v-3)color(blue)(-3)(v-3))`

`=v^2-3v" "-3v+9`

`=v^2-6v+9`
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So Equation(1) becomes

`2v-7" "=" "v^2-6v+9`

Add 7 and subtract `2v` from both sides giving:

`0=v^2-8v+16`

Notice that `-4-4=-8" and "(-4)xx(-4)=+16`

Factorising gives:

`(v-4)^2=0`

`=>v=+4`