Question

Factored form of x^2+10x+5

Answer 1

`\large\boxed{x^2+10x+5=\left(x+5+2\sqrt5\right)\left(x+5-2\sqrt5\right)}`

Explanation:

`\text{Use the quadratic formula:}\\\\ax^2+bx+c=a\left(x-(-b-√(b^2-4a))/(2a)\right)\left(x-(-b+√(b^2-4ac))/(2a)\right)\\======================================`

`\text{We have:}\ x^2+10x+5\to a=1,\ b=10\ \text{and}\ c=5\\\\\text{Substitute}\\\\b^2-4ac=10^2-4(1)(5)=100-20=80\\√(b^2-4ac)=√(80)=√(16\cdot5)=√(16)\cdot\sqrt5=4\sqrt5\\\\x_1=(-10-4\sqrt5)/(2(1))=-5-2\sqrt5\\\\x_2=(-10+4\sqrt5)/(2(1))=-5+2\sqrt5\\\\\bigg(x-\left(-5-2\sqrt5\right)\bigg)=\left(x+5+2\sqrt5\right)\\\\\bigg(x-\left(-5+2\sqrt5\right)\bigg)=\left(x+5-2\sqrt5\right)`