SOLUTION: solve this equation by completing the square: 1x^2/4+ 1x/16+ 1/8= 0

Question 248605: solve this equation by completing the square:
1x^2/4+ 1x/16+ 1/8= 0
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

To complete the square:

Transform the equation so that the variable terms are on one side and the constant term is on the other side.
If the leading coefficient is:
- a 1:
  1. Calculate 1/2 of the coefficient of x. Let's call this "q". (Don't forget to keep track of the sign of q.)
  2. Add to both sides of the equation
- Not a 1:
  1. Factor out the leading coefficient. (This can require some creative factoring.)
  2. Calculate 1/2 of the coefficient of x (inside the factor). Let's call this "q". (Don't forget to keep track of the sign of q.)
  3. Add inside the factor with the variables and add (leading coefficient)* to the other side of the equation.(This may seem that you are adding different things to each side. But with the leading coefficient in front of the factor on the left side, you are really adding (leading coefficient)* to both sides.)
Factor the trinomial (3-term expression) you have just created into

Since completing the square is easier if the leading coefficient is 1, I will start by multiplying both sides by 4:

(Note: When you are working with ellipses and hyperbolas (which are certain two variable equations), you will not be able to force a leading coefficient of 1 like we have here.)

Now that we have an easier equation to work with, let's go through the procedure:
1. Transform the equation...
Subtract 1/2 from each side:

2. Since the leading coefficient is 1, calculate "q" (1/2 of the coefficient of x):

3. Add to both sides. (Since our leading coefficient is 1, we can just add .

4. Factor the trinomial into

Now that we have completed the square we are in position to solve the equation. Normally the next step would be to find the square root of both sides of the equation. Then we would solve the two equations that result.

However this equation says that is a negative number. There are no real numbers whose square is negative. So there are no solutions (that are Real numbers).

If you want complex solutions then we will proceed:

or
Add } to (or subtract 1/8 from) each side:
or

In case you're interested, here is what completing the square looks like when the leading coefficient is not 1:

1. Transform the equation.
Subtract 1/8:

2. Since the leading coefficient is not 1,
2a. Factor out the leading coefficient. (This is where some creativity may be needed.):

2b. Calculate "q"

2c. Add in side the parentheses and (leading coefficient)* to the right side. :

which simplifies to:

3. Rewrite as a perfect square:

If we multiply both sides of this equation by 4, we end up with the same equation as before:

RELATED QUESTIONS
).1x^2-0.2x-0.9=0 the directions say: solve the equation by completing the... (answered by ReadingBoosters)

Solve using the principle of zero products (x - 2)(2x + 8)(3x + 9) = 0 this is what i... (answered by JBarnum)

Solve:... (answered by tommyt3rd)

3x-2/4+1=2x-3/2 I have tried for an hour to figure this problem. Below is how I am... (answered by stanbon)

Algebra 2 & Trigonometry Practice: Completing the Square #3 Page 1 www.jmap.org... (answered by lynnlo)

okay this problem says to solve by completing the square, but the odd numbers are... (answered by solver91311)

7x^2+1x-1=0 (answered by josgarithmetic)

{{{ 3x^2+5x-1=0 }}} Please help me solve this equation by completing the square (answered by jim_thompson5910)

Please help to solve this equation by completing the square: 3x^2 - x - 1 =... (answered by josmiceli)