Question

How do you complete the square for $ {x^2} + 12x $ ?

Answer 1

Hint: First we will reduce the equation further if possible. Then we will try to factorise the terms in the equation. Split the middle term and factorise the equation. Then equate the factors equal to zero and evaluate the value of the variable.

Complete step-by-step answer:
We will start off by writing the quadratic equation as a trinomial.
 $ {x^2} + 12x $
Now we will move $ 0 $ to the right-hand side. bvv vn hgvg jvh
 $ {x^2} + 12x = 0 $
Now we will divide the coefficient of the x-term by $ 2 $ .
 $ \dfrac{{12}}{2} = 6 $
Then square the result.
 $ {6^2} = 36 $
Now add the result to both the sides.
 $ {x^2} + 12x + 36 = 36 $
Factor the perfect square trinomial $ {x^2} + 12x + 36 $ on the left-hand side.
 $ {({x} + 6)^2} = 36 $
Now we will take the square root on both sides and solve for the value of $ x $ .
 $
  {{{(x + 6)}}} = \sqrt {36} \\
  \,\,\,\,\,\,\,(x + 6) = \pm 6 \\
   \;
  $
Now, the values of $ x $ can be,
 $
  x = - 6 + 6 \\
  \,\,\,\, = 0 \;
  $ or
 $
  x = - 6 - 6 \\
  \,\,\,\, = - 12 \;
  $
Hence, the values of $ x $ are $ 0, - 12 $ .
So, the correct answer is “ $ 0, - 12 $ ”.

Note: While splitting the middle term be careful. After splitting the middle term, do not solve all the equations simultaneously. Solve all the equations separately, so that you don’t miss any term of the solution. Check if the solution satisfies the original equation completely. If any term of the solution doesn’t satisfy the equation, then that term will not be considered as a part of the solution.