SOLUTION: Good Morning, I am trying to solve the following equations x2 - 2x - 13 = 0 i am not sure if i am finding the square root of each side completely here is the work i have comple

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Question 487112: Good Morning,
I am trying to solve the following equations x2 - 2x - 13 = 0
i am not sure if i am finding the square root of each side completely here is the work i have completed so far
The problem:
X2 - 2x - 13 = 0
Step #1
Move the constant term to the right side of the equation.
The constant term is - 13
X2 - 2x = 13
Step #2
Multiply each term in the equation by four times the coefficient of the term x
4x2 - (2x4 =) 8 = (13 x 4 =) 52
4x2 - 8 = 52
Step #3
Square the coefficient of the original x term and add it to both sides o the equation
Original Coefficient = 2 (2 squared =) 4
4x2 - 8 + 4 = 52 + 4
4x2 - 8 + 4 = 56
Step # 4
Take the square root of both sides
4x2 - 8 + 4 = 56
Please help me thank You
Bethany Keitzer
Found 2 solutions by nerdybill, Theo:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Your mistake is in steps 2 and 3. Review the "completing the square" section in your textbook.
.

Take 1/2 of the coefficient of the x term, square it, and add to both sides:

factor left:

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equation is x^2 - 2x - 13 = 0

it looks like you're trying to use the indian method for solving a quadratic equation.

i've used it, and i know that it works, but i haven't seen any great advantage to using it over the use of the quadratic formula that works every time and is fairly simple to use because all you do is supply the necessary values of a, b, and c to it and solve the formula as is.

the value of a is the coefficient of the x^2 term.
the vgalue of b is the coefficient of the x term.
the value of c is the constant term.

the standard form of the quadratic equation is :

ax^2 + bx + c = 0

the quadratic formula is:

x =

the indian method appears to be an offshoot from the completing the squares method.

it's main advantage is that you can work with the equation directly without having to make the coefficient of the x^2 equal to 1 as you would with the completing the squares method.

i'll work the problem through using the indian method and you can then follow that to see where you went wrong, if anywhere.

the steps of the indian method are shown below.

your equation is:

x^2 - 2x - 13 = 0

step 1:
Move the constant term to the right side of the equation

the constant term is equal to -13.
add it to both sides of the equation to get:
x^2 - 2x = 13

step 2:
Multiply each term in the equation by four times the coefficient of the x^2 term

the coefficient of the x^2 term is equal to 1.
multiply both sides of the equation by 4*1 = 4 to get:
4x^2 - 8x = 52

step 3:
Square the coefficient of the original x term and add it to both sides of the equation

the coefficient of the original x term is 2.
2 squared is equal to 4.
add it to both sides of your equation and you get:
4x^2 - 8x + 4 = 56

step 4:
Take the square root of both sides of the equation

the expression on the left side of your equation should be a perfect square.
this means that (ax + b)^2 = the expression on the left side of your equation.
you need to find the right factors, but they should be there if the method is to work.
i believe that a factor of (2x-2) should do it.
this is because (2x-2) * (2x-2) = 4x^2 - 4x - 4x + 4 which is equal to 4x^2 - 8x + 4 which is the expression on the left side of the equation that you are working with.
your equation becomes:
(2x-2)^2 = 56
take the square root of both sides of this equation to get:
2x-2 = +/- sqrt(56)

step 5:
Set the left side of the equation to the positive square root of the number on the right side and solve for x

you get:
2x - 2 = sqrt(56)
add 2 to both sides of the equation to get:
2x = sqrt(56) + 2
divide both sides of the equation by 2 to get:
x = (sqrt(56)+2)/2

step 6:
Set the left side of the equation to the negative square root of the number on the right side and solve for x.

you get:
2x - 2 = -sqrt(56)
add 2 to both sides of the equation to get:
2x = -sqrt(56) + 2
divide both sides of the equation by 2 to get:
x = (-sqrt(56)+2)/2

those should be your answers.

x = (sqrt(56)+2)/2
x = (-sqrt(56)+2)/2

plug those values for x into your original equation and the equation should be true which means that these values of x are solutions to your original equation.

i did that using my calculator and i was able to confirm that these values are good.

they are good, so your answer is:

x = (sqrt(56)+2)/2
x = (-sqrt(56)+2)/2

note that these factors can be reduced to:

x = 1 + sqrt(14)
x = 1 - sqrt(14)

this is because sqrt(56) = sqrt(4*14) = 2*(sqrt(14)

x = (sqrt(56)+2)/2 becomes x = (2*sqrt(14)+2)/2 which becomes x = sqrt(14) + 1 which becomes x = 1 + sqrt(14)

x = (-sqrt(56)+2)/2 becomes x = (-2*sqrt(14)+2)/2 which becomes x = -sqrt(14) + 1 which becomes x = 1 - sqrt(14)

your answer becomes:

x = 1 + sqrt(14)
x = 1 - sqrt(14)

this can also be written as:

x = 1 +/- sqrt(14)

dtheophilis@yahoo.com