# How do you solve x^2 + 10x + 25 = 0?

Apr 27, 2016

${\left(x + 5\right)}^{2}$

#### Explanation:

Notice that $5 \times 5 = 25 \text{ and } 5 + 5 = 10$

Everything in the equation is positive so everything in the factorisation is also positive

${x}^{2} + 10 x + 25 \text{ "->" "(x+5)(x+5)" "->" } {\left(x + 5\right)}^{2}$

$\overline{\underline{\text{'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}}$

Further explanation about how to multiply out brackets

Consider:$\text{ } \textcolor{b r o w n}{\left(x + 5\right)} \textcolor{b l u e}{\left(x + 5\right)}$

Write as:" "color(brown)(x color(blue)((x+5))+5color(blue)((x+5))
'.......................................................................................................

Consider:" "color(brown)(x color(blue)((x+5))

Multiply everything inside the bracket by $x$

$\textcolor{g r e e n}{{x}^{2} + 5 x}$
'.................................................................
Consider:" "color(brown)(5 color(blue)((x+5))

Multiply everything inside the bracket by $5$

$\textcolor{g r e e n}{5 x + 25}$
'...................................................................
Putting it all together

$\textcolor{g r e e n}{{x}^{2} + 5 x + 5 x + 25 = {x}^{2} + 10 x + 25}$