How do you solve 0=x2+10x+5?

2 Answers
George C.
May 12, 2016

x=−5±2√5

Explanation:

Complete the square and use the difference of squares identity:

a2−b2=(a−b)(a+b)

with a=(x+5) and b=2√5 as follows:

0=x2+10x+5

=(x+5)2−25+5

=(x+5)2−20

=(x+5)2−(2√5)2

=((x+5)−2√5)((x+5)+2√5)

=(x+5−2√5)(x+5+2√5)

Hence:

x=−5±2√5

Alan P.
May 12, 2016

x=−5+2√5XXXorXXXx=−5−2√5

Explanation:

The easiest way for this particular example is to use the quadratic formula:

For an equation of the form ax2+bx+c=0
the solutions are given by x=−b±√b2−4ac2a

For the given example

a=1
b=10 and
c=5

So
XXXx=−10±√102−4(1)(5)2(1)

XXXX=−10±4√52

XXXX=−5±2√5

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