Question

x( x +2) =8 solve completing the square​

Answer 1

Solution:

x(x+2)=8

=> x²+2x = 8

=> x²+2*x*1 = 8

=> x²+2*x*1+1² = 8+1²

/* adding 1 both sides */

=> (x+1)² = 9

=> (x+1) = ±√9

=> x+1 = ± 3

=> x = -1±3

Therefore,

x = -1+3 or x = -1-3

=> x = 2 or x = -4

••••

Answer 2

Answer :-

◾Here we have the question

x(x+2) = 8

▪️we have to solve it via multiplication

◾By multiplication of LHS we get

$\sf{x^2 + 2x = 8}$

◾Now subtracting 8 from both LHS and RHS

$\sf{ x^2 + 2x - 8 = 8 - 8}$

$\sf{ x^2 + 2x - 8 = 0}$

⏩So now we have got a quadratic equation , now solving it via Splitting middle term :-

$\sf{x^2 + 4x - 2x - 8 = 0}$

$\sf{ x(x + 4) -2(x + 4) = 0}$

$\sf{ (x+4)(x-2) = 0}$

⏩So we get

x = -4

or

x = 2

♦ So Answer

$\bold{x = 2 \:or \:-4 }$