Answer:
Solve Quadratic Equation by Completing The Square
Solving 2x2-6x-15 = 0 by Completing The Square .
Divide both sides of the equation by 2 to have 1 as the coefficient of the first term :
x2-3x-(15/2) = 0
Add 15/2 to both side of the equation :
x2-3x = 15/2
Now the clever bit: Take the coefficient of x , which is 3 , divide by two, giving 3/2 , and finally square it giving 9/4
Add 9/4 to both sides of the equation :
On the right hand side we have :
15/2 + 9/4 The common denominator of the two fractions is 4 Adding (30/4)+(9/4) gives 39/4
So adding to both sides we finally get :
x2-3x+(9/4) = 39/4
Adding 9/4 has completed the left hand side into a perfect square :
x2-3x+(9/4) =
(x-(3/2)) • (x-(3/2)) =
(x-(3/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-3x+(9/4) = 39/4 and
x2-3x+(9/4) = (x-(3/2))2
then, according to the law of transitivity,
(x-(3/2))2 = 39/4
Step-by-step explanation:
Basically, the answer is -1.622 and 4.622.
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