Question

Please Help?

Write 4-6 sentences describing how you can use the form of a quadratic equation to decide how it can most efficiently be solved. For each solution method (factoring, by inspection, taking a square root, completing the square, and the quadratic formula), formulate an equation that would be the most efficiently solved using that approach. Write a comprehensive solution process for each as though you are explaining it to a friend who is struggling with this topic.

I do not need 4-6 sentences, but just need main points so I can form my own sentences.

Answer 1

See explanation

Explanation:

The place to begin in attempting to solve a quadratic equation is to try to factorize it. If it can not be factorized, then look at the side of equation that contains the variable (x,b,m,n and so on). If that side is a perfect square, try to take square root of both sides.

Also, if the coefficient of the squared term in the equation is 1 and the coefficient of the middle term bearing the variable is an even number, then you can attempt to use completing the square method. Formula method can be adopted as a last resort.

x^2 -4x + 4 =0 can be solved by factorization

X(x-2) - 2(x-2) =0

Hence;

(x-2) (x-2) =0

x= 2 (twice)

(2x-2)^2 = 4 can be solved by taking square root

√[(2x-2)^2] = √4

2x-2 = 2

x= ±2

x^2 + 6x - 11 = 0 can be solved by completing the square

(x + 3)^2 = 11 + 3^2

(x + 3)^2 = 20 taking square root of both sides

x + 3 = ±√20

x + 3 = ±2√5

x= -3 ±2√5

2x^2 - x + 5 = 0 can be solved by formula method

Using

x= -b±√b^2 - 4ac/2a

a= 2, b = -1, c= 5

x= 1 ± √1 - 40/4

x= 1 ± √-39/4

x= 1 ± 39i/4