Question

Solving 6x²+9x-1=0 by completing the square root method produces an equation in the form of (x+h)²=k find H and K

Answer 1

The value of h is 9/12 and the value of k is 35/48

How to solve the equation?

The equation is given as:

6x^2 +9x - 1 = 0

Add 1 to both sides of the equations

6x^2 +9x - 1 + 1= 0 + 1

Evaluate the sum

6x^2 +9x =  1

Divide through the equation by 6

x^2 +9/6x =  1/6

Take the coefficient of x

k = 9/6

Divide by 2

k/2 = 9/12

Square both sides

(k/2)^2 = (9/12)^2

So, we add (9/12)^2 to both sides of the equation x^2 +9/6x =  1/6

x^2 +9/6x + (9/12)^2 =  1/6 + (9/12)^2

Next, we express the left-hand side as a perfect square

(x^2 + 9/12)^2 = 1/6 + (9/12)^2

The form of the equation is given as:

(x + h)^2 = k

So, we have:

h = 9/12

k = 1/6 + (9/12)^2

Simplify

k = 1/6 + (3/4)^2

Evaluate the exponent

k = 1/6 + 9/16

This gives

k = (8 + 27)/48

Evaluate

k = 35/48

Hence, the value of h is 9/12 and the value of k is 35/48

Read more about completing the square at:

brainly.com/question/4331586

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