# How do you solve h^2=-3h+54?

Mar 30, 2018

$h = - 9 \mathmr{and} h = 6$

#### Explanation:

Rearrange to get

${h}^{2} + 3 h - 54 = 0$

Factorise

$\left(h + 9\right) \left(h - 6\right) = 0$

$h + 9 = 0 \mathmr{and} h - 6 = 0$

$h = - 9 \mathmr{and} h = 6$

Mar 30, 2018

$h = - 9 \text{ or } h = 6$

#### Explanation:

$\text{arrange the equation in standard form}$

$\Rightarrow {h}^{2} + 3 h - 54 = 0 \leftarrow \textcolor{b l u e}{\text{in standard form}}$

$\text{the factors of - 54 which sum to + 3 are + 9 and - 6}$

$\Rightarrow \left(h + 9\right) \left(h - 6\right) = 0$

$\text{equate each factor to zero and solve for h}$

$h + 9 = 0 \Rightarrow h = - 9$

$h - 6 = 0 \Rightarrow h = 6$

Mar 30, 2018

$h = - 9 , 6$.

#### Explanation:

We have,

$\textcolor{w h i t e}{\times x} {h}^{2} = - 3 h + 54$

$\Rightarrow {h}^{2} + 3 h - 54 = \cancel{- 3 h} \cancel{+ 54} \cancel{+ 3 h} \cancel{- 54}$ [Add $3 h - 54$ to both sides]

$\Rightarrow {h}^{2} + 3 h - 54 = 0$

$\Rightarrow {h}^{2} + \left(9 - 6\right) h - 54 = 0$ [Break $3$ as $9 - 6$]

$\Rightarrow {h}^{2} + 9 h - 6 h - 54 = 0$

$\Rightarrow h \left(h + 9\right) - 6 \left(h + 9\right)$ [Group Like Terms]

$\Rightarrow \left(h + 9\right) \left(h - 6\right) = 0$ [Group Again]

So, If,

$h + 9 = 0 \Rightarrow h = - 9$

and if,

$h - 6 = 0 \Rightarrow h = 6$

Hence Explained.