Question

Show by completing the square that x²+5x-10=(x+5/2)²-65/4​

Answer 1

x = -10

Given :

`x^(2) +5x-10 = (x+5/2)^(2) -65/4`

`x^(2) +5x-10 = (x+5/2)^(2) -65/4\\x^(2) +5x-10 = (x+5)^(2) /4-65/4\\4x^(2) +20x-40 = (x+5)^(2) -65\\4x^(2) +20x-40 = x^(2) +25-10x -65\\4x^(2) +20x-40 = x^(2) -10x-40\\4x^(2) -x^(2) +20x+10x-40+40=0\\3x^(2) +30x=0\\3(x^(2) +10x)=0\\x^(2) +10x=0\\x^(2) =-10x\\x=-10`