x²+(x+5)²=625,Find the roots of the given equation by the method of perfect square.
Answers
2x²+25+10x = 625
2x²+10x= 600
2x²+10x-600 =0
x²+5x-300=0
x²+20x-15x-300=0
x(x+20)-15(x+20)=0
x+20=0 ; x-15=0
x=-20 ; x=15
We will rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2+(x+5)^2-(625)=0
Pull out like factors :
2x2 + 10x - 600 = 2 • (x2 + 5x - 300)
Factoring x2 + 5x - 300
Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 20
x2 - 15x + 20x - 300
Add up the first 2 terms, pulling out like factors :
x • (x-15)
Add up the last 2 terms, pulling out common factors :
20 • (x-15)
Add up the four terms of step 4 :
(x+20) • (x-15)
Which is the desired factorization
2 • (x + 20) • (x - 15) = 0
x = ( -5 ± 35) / 2
x =(-5+√1225)/2=(-5+35)/2= 15