How do you solve the quadratic equation 2x^2+10x+10=0?
2 Answers
Apr 12, 2018
Explanation:
"take out a "color(blue)"common factor "2
rArr2(x^2+5x+5)=0
"there are no whole number factors of + 5 which sum to + 5"
"solve "x^2+5x+5=0" using the "color(blue)"quadratic formula"
•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)
"with "a=1,b=5" and "c=5
rArrx=(-5+-sqrt(25-20))/2=(-5+-sqrt5)/2
rArrx=-5/2+-1/2sqrt5larrcolor(red)"exact solutions"
Apr 12, 2018
The answer is
Explanation:
- The first step is to take a factor of 2:
2x^2+10x+10=0
2(x^2+5x+5)=0 - Then divide both sides by 2:
(2(x^2+5x+5))/2=0/2
x^2+5x+5=0 - Now subtract both sides by 5:
x^2+5x+5-5=0-5
x^2+5x=-5 - Now you have to complete the square:
x^2+5x+(5/2)^2=-5+(5/2)^2 - Now factorize the LHS (Left Hand Side):
(x+5/2)^2=-5+(5/2)^2 - Simplify the RHS (Right Hand Side):
(x+5/2)^2=-5/1+5^2/2^2
(x+5/2)^2=(-5/1*4/4)+25/4
(x+5/2)^2=-20/4+25/4
(x+5/2)^2=5/4 - Now solve for
x .
x+5/2=+-sqrt(5/4)
x=-5/2+-sqrt(5/4)
There may be other ways to do it, but this is the way that I solved this.