How exactly do you solve this equation by completing the square: 2x² - 4x - 3 = 0
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# How exactly do you solve this equation by completing the square: 2x² - 4x - 3 = 0

[From: ] [author: ] [Date: 11-10-07] [Hit: ]
-----------------------------EDIT: Your book probably felt like being lazy and using the quadratic formula to get a quick solution. If you let:x^2 - 2x - (3/2) = 0Then...x = [2 ± √(4 - 4 *1 * -3/2)]/2x = [2 ± √(4 + 6)]/2x = [2 ± √(10)]/2Which can be simplified to........
First, get the value in front of x² by itself by dividing everything by the coefficient before it, yielding:

x² - 2x = 3/2

Now you have to add the value of (b/2)² to both sides, where b is the values in front of the x term, so:

x² - 2x + 1 = 3/2 + 1

Now you can factor the left to (x + b/2)²:

(x - 1)² = 5/2

Take the square root of both sides, keeping in mind that a square root produces a positive and negative result:

x - 1 = ±√(5/2)

Solve for x:

x = 1 ± √(5/2)

Hope that helps.

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EDIT: Your book probably felt like being lazy and using the quadratic formula to get a quick solution. If you let:

x^2 - 2x - (3/2) = 0

Then...

x = [2 ± √(4 - 4 *1 * -3/2)]/2
x = [2 ± √(4 + 6)]/2
x = [2 ± √(10)]/2

Which can be simplified to...

x = 1 ± √(10)/2
x = 1 ± √(10/4)
x = 1 ± √(5/2)

That's the same thing.

Also, neat trick Robert, shame it doesn't work...

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You were taught to take 1/2 of "b", then square that result and add it to both sides.
In this problwm you have to divide by "a" first. Notice this creates a fraction with the -3.

Here is a method not taught anymore. NO FRACTIONS till the last step.

2x² - 4x - 3 = 0
ax^2+bx+c=0
In this problem a=2 and b=-3
Here is what you do:
Multiply every term by 4a..........4a=....4(2)=..............8

8(2x² - 4x - 3 = 0)

16x^2-32x-24=0

16x^2-32x=+24

16x^2-32x+9=+24+9.....You just created a Perfect Square Trinomial which is the pupose
......................................… Completing The Square................Now factor the left side
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