Question

Solve the quadratic equation by completing the square.
2x^2 + 10x - 2 = 0

Answer 1

2x^2 + 10x - 2 = 0
a b c

get rid of c put it on the right then divide by a to get rid of a

2x^2 + 10x = 2
x^2 + 5x = 1
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completing the square comes from a perfect square
(x+a)*(x+a) when you distribute
x^2+2ax+a^2
NOTE this is not the same a as above new a new variable.
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wee need to add something to
x^2 + 5x = 1 to make it a perfect square.
x^2 +2ax +a^2
If we put the distrubets (x+a)^2 under it we see that
5=2a aka the coeeficient
so if we solve for a

a=5/2
further more we see that a has to be squared

so we add a^2 to both sides


x^2 + 5x +(5/2)^2 = 1+ (5/2)^2


now since x^2 + 5x +(5/2)^2 is a perfect square
(x+a)^2
and we know a=5/2

we make left hand a perfect square by plugin in a

(x+5/2)^2= 1+ (5/2)^2

we take square root now

(x+5/2)= plus or minussqrt(1+ (5/2)^2)


and solve normally now