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

1 Answer
Apr 27, 2016

Answer:

#(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)#