Question

How do you find the missing value to complete the square \[{x^2} + 2x\]?

Answer 1

Hint: Here it is given that there is a quadratic equation whose one term is missing, to solve this question we should memorize the general equation of quadratic, and after comparison we can obtain the missing term. The general equation for quadratic can be written as \[{(a + b)^2} = {a^2} + 2ab + {b^2}\], after comparing our equation with this equation we can get the missing term.

Formulae Used: \[ {(a + b)^2} = {a^2} + 2ab + {b^2}\] for any value of the variables.

Complete step by step solution:
The given question is to find the missing term from the equation \[{x^2} + 2x\], on solving we get:
Firstly we have to see the general equation of quadratic which is:
\[ \Rightarrow {(a + b)^2} = {a^2} + 2ab + {b^2}\]
On comparing our equation with the general equation we get:
\[ \Rightarrow a = x,b = ?\]
Here we see that on comparison the “b” term is missing in the question to find that let us assume value of “b” is “z”, on solving we get:
\[
   \Rightarrow 2x = 2ab(\text{comparison with general equation}) \\
   \Rightarrow 2x = 2(x)(z)\left[ {\text{we assumed b = z and from comparison a = x}} \right] \\
   \Rightarrow z = \dfrac{{2x}}{{2x}} = 1 \\
 \]
Hence we got the value of “b” which is equal to “z” and equals to one.
Now the missing term is:
\[ \Rightarrow {b^2} = {1^2} = 1\]
Hence the complete quadratic equation will be:
\[ \Rightarrow {x^2} + 2x + 1\]

Note: Here this question needs to be solved by the comparison method only, because to complete the equation we have to relate it with the general term. Another method that we can use here is by completing the equation by assuming the value, and we have to add and subtract that value in the equation. After completing the equation the value leftover will be our missing value.