Question

Complete the square x^2 + 8 x + 6

Answer 1

Step-by-step explanation:

Alternate forms:

x (x + 8) + 6 = 0

(x + 4)^2 - 10 = 0

1/10 (x + 4)^2=1

Solutions:

x = -4 - sqrt√(10)

x = sqrt√(10) - 4

Answer 2

As , we know the given question is in a form of quadratic equation, So the general form of quadratic equation is: ax² + bx + c = 0

Hence, x² + 8x + c = 0 [ Here , a = 1 ].

Now, We have to solve this quadratic equation by completing it's square, We know the middle term i.e, bx the coefficient of x which is = b , that will be divided by its half , thus = (b÷2)²

Than, The resulted division will be obtained in both positive and negative ( don't cross it to make zero ). For example( reference in the above attachment ), Here's, bx = 8x, so its came 4 after using (b÷2)².

Write in both, +4 and -4. ( don't do it to make zero, let it be remain like this for next step ).

Now, see that it's in positive or negative, which is taking it's perfec square of the whole expression. For example( reference in the above attachment ), Here's, x² + 8x - (4)² = (x-4)² [ Here, (a-b)² = a² + 2ab - b² ].

Proceeding towards next step, (x-4)² + (4)² = -6 [ Now, solve this whole expression to obtain the value of x ].