Question

Solve the quadratic equations to give your answer correct to 2 decimal places. 2x^2-10x+5=0

Answer 1

Answer:

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Step-by-step explanation:

Divide both sides of the equation by  2  to have 1 as the coefficient of the first term :

  x2-5x-(5/2) = 0

Add  5/2  to both side of the equation :

  x2-5x = 5/2

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  5/2  +  25/4   The common denominator of the two fractions is  4   Adding  (10/4)+(25/4)  gives  35/4

 So adding to both sides we finally get :

  x2-5x+(25/4) = 35/4

Adding  25/4  has completed the left hand side into a perfect square :

  x2-5x+(25/4)  =

  (x-(5/2)) • (x-(5/2))  =

 (x-(5/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2-5x+(25/4) = 35/4 and

  x2-5x+(25/4) = (x-(5/2))2

then, according to the law of transitivity,

  (x-(5/2))2 = 35/4

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(5/2))2   is

  (x-(5/2))2/2 =

 (x-(5/2))1 =

  x-(5/2)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-(5/2) = √ 35/4

Add  5/2  to both sides to obtain:

  x = 5/2 + √ 35/4

Since a square root has two values, one positive and the other negative

  x2 - 5x - (5/2) = 0

  has two solutions:

 x = 5/2 + √ 35/4

  or

 x = 5/2 - √ 35/4

Note that  √ 35/4 can be written as

 √ 35  / √ 4   which is √ 35  / 2