Given: \(\sqrt{3}x^2+10x+7\sqrt{3}=0\)
To find: the roots of the following quadratic (if they exist) by the method of completing the square.
Solution: We have to make the quadratic equation a perfect square if possible or sum of perfect square with a constant.
Step 1: Make the coefficient of x2 unity.In the equation
\(\sqrt{3}x^2+10x+7\sqrt{3}=0\),
The coefficient of x2 is \(\sqrt{3}\)
So to make the coffecient of x2 equals to 1.
divide the whole equation by \(\sqrt{3}\) .
The quadratic equation now becomes:
Step 2: Shift the constant term on RHS,
Step 3: Add square of half of coefficient of x on both the sides.
Step 4: Apply the formula, (a + b)2 = a2 + 2ab + b2 on LHS and solve RHS,
Here a = x and \(b = \frac{5}{\sqrt{3}}\)
As RHS is positive, the roots exist.
Step 5: take square root on both sides,