Question

x^2+16x-9=0 by completing squaring method

Answer 1

Answer:

x = ±√73 - 8

Step-by-step explanation:

'Completing the square'

⇒ Consider the polynomial given in the question.

• x² + 16x - 9 = 0

⇒ Add 9 to both sides.

• x² + 16x = 9

⇒ Now to complete the square, we have to add the square of half the coefficient of x to both sides. Here the coefficient of x is 16, so (16/2)² = 8² = 64 should be added.

• x² + 16x + 64 = 9 + 64

⇒ Factorise the LHS.

• (x + 8)² = 73

⇒ Take the square roots of both.

• x + 8 = ±√73

⇒ Now subtract 8 from both sides.

• x = ±√73 - 8
• x = √73 - 8  OR  x = -√73 - 8

⇒ Thus the value of x is √73 - 8 or -√73 - 8.