Question

3+ х = х2 + 3x
rewrite by completing the square

Answer 1

Explanation:

Completing square:

3 + x = x² + 3x

x² + 3x = x + 3

Step 1: Subtract 'x' from both sides

x² + 3x - x = 3

x² + 2x = 3

Step 2: Divide the coefficeint of x by 2 and square the result

2 ÷ 2 = 1

1² = 1

Step 3: Now add 1 to both the sides

x² + 2x + 1 = 3 + 1

x² + 2x + 1 = 4

The LHS of the equation is in the form a² + 2ab + b² = (a +b)²

(x + 1)² = 2²

Take square root,

x + 1 = ± 2

x + 1 = 2 ;x + 1 = -2

x = 2 - 1 ; x = - 2-1

x = 1 ; x = -3

Solution: x = 1,-3