Question

consider the equation x square + 10x = 15
a) what # must be added to x square + 10 to complete the square?
b) solve the equation x square + 10 =15 by adding that # on both sides n using the method shown in example one
c) solve the quation x square + 10x = 15 using the quadratic formula

Answer 1

add 25 on left hand side

Answer 2

so you get (x+5)^2=15

Answer 3

\[x^2+10x=15\] to complete the square think
half of ten is five then write
\[(x+5)^2=15+\] and \[5^2 = 25\] to get
\[(x+5)^2=15+25=40\]

Answer 4

so now you have \[(x+5)^2=40\] and \[x+5=\pm \sqrt{40}\]so
\[x=-5\pm\sqrt{40}\]

Answer 5

if you have to write in simplest radical form
\[\sqrt{40}=\sqrt{4\times 10}=\sqrt{4}\times \sqrt{10}=2\sqrt{10}\]

Answer 6

so 'final answer" is
\[-5\pm2\sqrt{10}\]