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

Jul 26, 2016

$v = + 4$

#### Explanation:

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

Square both sides

$2 v - 7 = {\left(v - 3\right)}^{2}$

$2 v - 7 = \left(v - 3\right) \left(v - 3\right)$ ......................Equation(1)
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Consider $\textcolor{b l u e}{\left(v - 3\right)} \textcolor{b r o w n}{\left(v - 3\right)}$

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

$\textcolor{b r o w n}{\textcolor{b l u e}{v} \left(v - 3\right) \textcolor{b l u e}{- 3} \left(v - 3\right)}$

$= {v}^{2} - 3 v \text{ } - 3 v + 9$

$= {v}^{2} - 6 v + 9$
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So Equation(1) becomes

$2 v - 7 \text{ "=" } {v}^{2} - 6 v + 9$

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

$0 = {v}^{2} - 8 v + 16$

Notice that $- 4 - 4 = - 8 \text{ and } \left(- 4\right) \times \left(- 4\right) = + 16$

Factorising gives:

${\left(v - 4\right)}^{2} = 0$

$\implies v = + 4$