Question

solution of x^2-6x+7=0 by completing the square

Answer 1

Answer:

Let's find the solution step by step.

Step 1: Rearrange the equation in the form of ax2 + bx = c, if necessary.

⇒ x2 + 6x = 7

Step 2: Add (b/ 2)2 on both the sides of the equation, b = 6 (coefficient of x)

⇒ x2 + 6x + (6/ 2)2 = 7 + (6/ 2)2

Step 3: Factorise the sides using algebraic identity (a + b)2 into perfect squares.

⇒ (x + 6/ 2 )2 = 7 + (3)2

Step 4: Square root on both the sides.

⇒ √ (x + 6/ 2 )2 = √ 16

Step 5: Solve for x.

⇒ x + 3 = ± 4

⇒ x = ± 4 - 3

⇒ x = - 7 or 1

Thus, the set of solutions for the equation x2 + 6x = 7 by completing the squares, by completing the squares is -7 and 1.

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