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solve the equation 4x^2-12x+3=0 by completing the square

Sagot :

2260945

Answer:

3/2 + 1/2 √6 or 3/2 + -1/2 √6

Step-by-step explanation:

Subtract 3 from both sides.

4x2−12x+3−3=0−3

4x2−12x=−3

Since the coefficient of 4x^2 is 4, divide both sides by 4.

4x2−12x/4 = −3/4         x2−3x= −3/4

The coefficient of -3x is -3. Let b=-3.

Then we need to add (b/2)^2=9/4 to both sides to complete the square.

Add 9/4 to both sides

x2−3x + 9/4 = −3/4 + 9/4

x2−3x + 9/4 = 3/2

Factor left side.

(x−3/2)2 = 3/2

Take square root.

x−3/2 = ± √3/2

Add 3/2 to both sides.

x−3/2 + 3/2 = 3/2 ± √3/2

x = 3/2 ± √3/2

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