Need help with Quadratic Equation alternative?

Question

Alternative method for quadratic equations

Problem x₂ + 12X – 64 =0

Step 1 move the constant

X₂ + 12X = 64

Step 2 multiply both sides by 4 times the coefficient of X₂

4(X₂ +12X) = 4(64)

4X₂ + 48X = 256

Step 3 Square the original X term and add to both sides

4X₂ + 48X +144 = 256 +144

4X₂ + 48X +144 = 400

Step 4 Take the square root of both sides

6.928X + 12 = 20

Step 5 solve for x and –x

I know that step 4 should be 2X +12=20 but 2 is not the square root of 48.

Where did I go wrong?

Please don’t sent me to the online quadratic equation solvers. I know where they are but that is not the method I am supposed to be using. All other problems have worked out using this method. How do I get from 48 to 2 by taking the square root?

Answer 1

taking the square root of both sides is where you went wrong

4x^2 + 48x + 144  =

4(x + 6)^2

square root that

2(x + 6) = 2x + 12

trust me, just use the quad formula. You're much more likely to make a mistake using this method

Answer 2

actually the square root of 4x^2 + 48x +144

IS 2x+12

(2x+12)(2x+12)

= 4x^2 + 24x + 24x + 144

= 4x^2 + 48x + 144

When taking the square root of an expression with more than one term, (ie with a - or + between it) you can't take the square root of both seperately

Answer 3

You have 4X^2 + 48X +144 which is a square, not 48X +144.

(2X+12)^2 = (2X+12)(2X+12)

                = 2X*2X + 2*12*X + 2*12*X + 12*12

                = 4X^2 + 48*X + 144

So the square root you want is 2X+12.

Answer 4

i am not sure of  this method but all Quadratic eqn  have solution like this  ax^2+bx+c = 0 has  roots or solution

-b + - sqrt b^2-4ac / 2a in our  case x^2+12x-64 = 0 i.e. a =1,b =12 c= - 64

-12 + - sqrt 12^2 + 4.64 /2 = -12+- sqrt400 /2  

-12 + - 20/2  hence  solution is 4 and -16.