SOLUTION: Which method should be used (factoring, square root property, completing the square, and the quadratic formula) to solve each of the following quadratic equations. Each method ca

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Question 1094450: Which method should be used (factoring, square root property, completing the square, and the quadratic formula)
to solve each of the following quadratic equations. Each method can be used only ONCE and why that method?

A) 4x^2 – 27 = 0
B) 4x^2 – 8x – 5 = 0
C) 4x^2 – 8x – 12 = 0
D) 4x^2 – 9x – 7 = 0
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A) 4x^2 – 27 = 0
Square root property;
4x%5E2=27
x%5E2=27%2F4
x=0%2B-+%283%2F2%29sqrt%283%29


B) 4x^2 – 8x – 5 = 0
C) 4x^2 – 8x – 12 = 0
D) 4x^2 – 9x – 7 = 0
-
Try to factorize if you have the patience or can quickly see; otherwise, quadratic formula.



You might want to try completing the square for B and C.
4x%5E2-8x=5
4%28x%5E2-2x%29=5
4%28x%5E2-2x%2B1-1%29=5
4%28%28x-1%29%5E2-1%29=5
4%28x-1%29%5E2-4=5
4%28x-1%29%5E2=9
%28x-1%29%5E2=9%2F4
x-1=0%2B-+3%2F2
x=1%2B-+3%2F2

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Which method should be used (factoring, square root property, completing the square, and the quadratic formula)
to solve each of the following quadratic equations. Each method can be used only ONCE and why that method? 

A) 4x^2 – 27 = 0            I'd use factoring.

B) 4x^2 – 8x – 5 = 0        completing the square, or the quadratic formula could be used.

C) 4x^2 – 8x – 12 = 0       As the first step, I'd divide both sides by 4 and then apply completing the square.

D) 4x^2 – 9x – 7 = 0        Quadratic formula.


Different people may have different preferences.

Ideally  if you know all these methods equally well and can apply any of them. You may even apply DIFFERENT methods to check yourself.


---------------
On solving quadratic equations, see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
    - HOW TO complete the square - Learning by examples
    - HOW TO solve quadratic equation by completing the square - Learning by examples
    - Solving quadratic equations without quadratic formula
    - Who is who in quadratic equations
    - Using Vieta's theorem to solve qudratic equations and related problems
    - Using quadratic equations to solve word problems
    - HOW TO solve the problem on quadratic equation mentally and avoid boring calculations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Quadratic equations".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Which method should be used (factoring, square root property, completing the square, and the quadratic formula)
to solve each of the following quadratic equations. Each method can be used only ONCE and why that method?

A) 4x^2 – 27 = 0
B) 4x^2 – 8x – 5 = 0
C) 4x^2 – 8x – 12 = 0
D) 4x^2 – 9x – 7 = 0
Easiest methods:

A) 4x^2 – 27 = 0 <======== Square-root property

B) 4x^2 – 8x – 5 = 0 <==== FACTORING, as this TRINOMIAL CAN be factored

C) 4x^2 – 8x – 12 = 0 <=== Factor out GCF, 4, and then use FACTORING, as the resulting TRINOMIAL can be factored

D) 4x^2 – 9x – 7 = 0 <==== Can't be factored so complete the square, or use the quadratic formula

Since each method can only be used once, then I'd factor out GCF, 4 and then complete the square for C), 

and I'd use the quadratic equation formula for D), or vice-versa. So, there you have it.