
How do you solve the equation $4{x^2} = 20x - 25$by completing the square?
Answer
442.5k+ views
Hint: Completing the square is the method which represents the quadratic equation as the combination of the quadrilateral used to form the square and it is the basis of the method discovers the special value which when added to both the sides of the quadratic which creates the perfect square trinomial. Here we will take the given expression and check for the perfect square or the value to be added. It becomes very easy to form the complete square if the given expression itself is the perfect square.
Complete step-by-step solution:
Take the given expression: $4{x^2} = 20x - 25$
Move all the terms from the right hand side of the equation to the left hand side of the equation. Remember when you move any term from one side to another, then the sign of the term also changes. Positive terms become negative and the negative term becomes positive.
$4{x^2} - 20x + 25 = 0$
The above equation can be re-written as: ${(2x)^2} - 2(2x)(5) + {(5)^2} = 0$
The above equation can be framed in the form of ${a^2} - 2ab + {b^2} = {(a - b)^2}$
${(2x - 5)^2} = 0$
Take the square root on both sides of the equation.
$\sqrt {{{(2x - 5)}^2}} = 0$
Square and square root cancel each other on the left hand side of the equation.
$ \Rightarrow 2x - 5 = 0$
Make “x” the subject and move constants on the right hand side of the equation.
$ \Rightarrow 2x = 5$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$ \Rightarrow x = \frac{5}{2}$
This is the required solution.
Note: Be careful about the sign convention and remember when you move any term from one side to another then the sign of the term also changes. Positive term becomes the negative and the negative term becomes positive.
Complete step-by-step solution:
Take the given expression: $4{x^2} = 20x - 25$
Move all the terms from the right hand side of the equation to the left hand side of the equation. Remember when you move any term from one side to another, then the sign of the term also changes. Positive terms become negative and the negative term becomes positive.
$4{x^2} - 20x + 25 = 0$
The above equation can be re-written as: ${(2x)^2} - 2(2x)(5) + {(5)^2} = 0$
The above equation can be framed in the form of ${a^2} - 2ab + {b^2} = {(a - b)^2}$
${(2x - 5)^2} = 0$
Take the square root on both sides of the equation.
$\sqrt {{{(2x - 5)}^2}} = 0$
Square and square root cancel each other on the left hand side of the equation.
$ \Rightarrow 2x - 5 = 0$
Make “x” the subject and move constants on the right hand side of the equation.
$ \Rightarrow 2x = 5$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$ \Rightarrow x = \frac{5}{2}$
This is the required solution.
Note: Be careful about the sign convention and remember when you move any term from one side to another then the sign of the term also changes. Positive term becomes the negative and the negative term becomes positive.
Recently Updated Pages
What percentage of the area in India is covered by class 10 social science CBSE

The area of a 6m wide road outside a garden in all class 10 maths CBSE

What is the electric flux through a cube of side 1 class 10 physics CBSE

If one root of x2 x k 0 maybe the square of the other class 10 maths CBSE

The radius and height of a cylinder are in the ratio class 10 maths CBSE

An almirah is sold for 5400 Rs after allowing a discount class 10 maths CBSE

Trending doubts
Change the following sentences into negative and interrogative class 10 english CBSE

Difference between mass and weight class 10 physics CBSE

What is Commercial Farming ? What are its types ? Explain them with Examples

Which state has the longest coastline in India A Tamil class 10 social science CBSE

Distinguish between coming together federations and class 10 social science CBSE

10 examples of evaporation in daily life with explanations
