Question

1. Find the solution sets for the following equations A.2x²+x-4=0 B. x²-2x-6=0 (by completing square method) (by quadratic formula method)​

Answer 1

A) Completing squares we got the solutions:

x = -1/4 ±  √(33/16)

B) Using the quadratic formula method we got:

x =  1  ± √7

How to complete squares?

Remember the relation:

(a + b)^2 = a^2 + 2ab + b^2

Now, we have the quadratic equation:

2x^2 + x - 4 = 0

First, we can rewrite our equation as:

(√2*x)^2 + 2*(1/2)*x - 4 = 0

Now, we can add and subtract (1/√2*2)^2 so we get:

(√2*x)^2 + 2*(1/2)*x - 4 +  (1/√2*2)^2 -  (1/√2*2)^2 =0

[(√2*x)^2 + 2*(1/√2*2)*(√2*x) +  (1/√2*2)^2] - 4 -  (1/√2*2)^2 = 0

Now we can complete squares inside the first part:

(√2*x + (1/√2*2))^2 - 4 - (1/√2*2)^2 = 0

(√2*x + (1/√2*2))^2 - 4 - 1/8 = 0

(√2*x + (1/√2*2))^2 = 4 + 1/8 = 33/8

Now we can solve this for x:

(√2*x + (1/√2*2)) = ±√(33/8)

√2*x  = -  (1/√2*2) ± √(33/8)

x = ( -(1/√2*2) ± √(33/8))/√2

x = -1/4 ±  √(33/16)

These are the two solutions of x.

How to use the quadratic formula method?

For a general quadratic equation:

a*x^2 + b*x + c = 0

The solutions are given by:

x = (-b ± √(b^2 - 4ac))/2a

In this case, we have:

x^2 - 2x - 6 = 0

Then the solutions are:

x = (2 ± √( (-2)^2 - 4*1*(-6))/2*1

x = (2 ± √(4 + 24))/2

x = 1  ± √(28)/2

x =  1  ± √7

If you want to learn more about quadratic equations

brainly.com/question/1214333

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