Question

(x-5)^2+3(x-5)+9=0 what is solution​

Answer 1

NO REAL SOLUTION

Explanation:

`(x-5)^2=x^2-2(x)(5)+5^2=x^2-10x+25\\\\\text{used}\ (a-b)^2=a^2-2ab+b^2\\\\3(x-5)=(3)(x)+(3)(-5)=3x-15\\\\\text{used the distributive property}\ a(b+c)=ab+ac`

`(x-5)^2+3(x-5)+9=0\\\\x^2-10x+25+3x-15+9=0\qquad\text{combine like terms}\\\\x^2+(-10x+3x)+(25-15+9)=0\\\\x^2-7x+19=0\\\\\text{Use the quadratic formula:}\\\\a=1,\ b=-7,\ c=19\\\\b^2-4ac=(-7)^2-4(1)(19)=49-76=-27<0\\\\\text{NO REAL SOLUTION}`