Question

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

Answer 1

`(x+5)^2`

Explanation:

Notice that `5xx5=25" and "5+5=10`

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

`x^2+10x+25" "->" "(x+5)(x+5)" "->" "(x+5)^2`

`bar(underline("'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"))`

Further explanation about how to multiply out brackets

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

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`

`color(green)(x^2+5x)`
'.................................................................
Consider:`" "color(brown)(5 color(blue)((x+5))`

Multiply everything inside the bracket by `5`

`color(green)(5x+25)`
'...................................................................
Putting it all together

`color(green)(x^2+5x+5x+25 = x^2+10x+25)`