Answer

Verified

387.6k+ views

**Hint:**To avoid arithmetic multiplying fraction multiply the given equation $2{{x}^{2}}-3x+1=0$ by $'8'$

Use the difference of square identity that is ${{a}^{2}}-{{b}^{2}}=\left( a-b \right)\left( a+b \right)$

For simplifying the problem replace $'x'$ terms by $'a'$ and $'b'$

Place $'x'$ term on the left side to find the value of $'x'$ and the coefficient on the right side.

**Complete step by step solution:**As per the given equation is $2{{x}^{2}}-3x+1=0$

Here to avoid arithmetic involving fraction multiply the whole equation by $'8'$

$8\left( 2{{x}^{2}}-3x+1 \right)=0\times 8$

So, after multiplying the modified equation will be.

$16{{x}^{2}}-24x+8=0$

Here you can write $'+9-1'$on the place of $'+8'$

$16{{x}^{2}}-24x+9-1=0$

Here in above equation, $16{{x}^{2}}-24x+9$

${{\left( a-b \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}$ formula

Here in $16{{x}^{2}}-24x+9$

$a=4x$

And $b=3$

Therefore, process this step:

${{\left( 4x-3 \right)}^{2}}-1=0$

Here, $'1'$ can be written as $'{{1}^{2}}'$ because ${{1}^{2}}=1$

So,

${{\left( 4x-3 \right)}^{2}}-{{1}^{2}}=0$

Now in above equation you can apply ${{a}^{2}}-{{b}^{2}}=\left( a-b \right)\left( a+b \right)$ identity.

Here, $a=4x-3$

$b=1$

Therefore,

$\left[ \left( 4x-3 \right)-1 \right]\left[ \left( 4x-3 \right)+1 \right]=0$

Opening, the bracket to solve the equation or simplifying the equation.

$\left[ 4x-3-1 \right]\left[ 4x-3+1 \right]=0$

$\left( 4x-4 \right)\left( 4x-2 \right)=0$

Choose common term from each equation in $\left( 4x-4 \right)$ $'4'$ is common term as it divides by both $'4x'$ and $'4'$ and in ${{2}^{nd}}$ equation $\left( 4x-2 \right)'2'$ is common term as it divides by $'4x'$ and $'2'$ both.

So,

$\left[ 4\left( x-1 \right) \right]\left[ 2\left( 2x-1 \right) \right]=0$

Multiply $4\times 2=8$

$8\left( x-1 \right)\left( 2x-1 \right)=0$

For finding the value of $x,$

$8\left( x-1 \right)=0$ or $8\left( 2x-1 \right)=0$

$8x-8=0$ or $16x-8=0$

$x=\dfrac{8}{8}$ or $x=\dfrac{8}{16}$

$x=1$ and $x=\dfrac{1}{2}$

The value of $x$ is $1$ and $\dfrac{1}{2}$

**Additional Information:**

In order to use the completing the square method, the value of $a$ in quadratic equation must be $1.$ If it is not $1,$ you will have to use AC method or the quadratic formula in order to solve for $x.$

Completing the square is a method used to solve quadratic equation $a{{x}^{2}}+bx+c$ where a must be $1.$ The goal is to force a perfect square trinomial on one side and then solve for $'x'$ by taking the square root of both sides.

**Note:**

Use the difference of square identity that is ${{a}^{2}}-{{b}^{2}}=\left( a-b \right)\left( a+b \right)$ make the equation into difference of square identity.

As you have multiplied the given equation by $'8'$ to avoid too much arithmetic involving fraction.

The digit $'8'$ is preferred to multiply because $8={{2.2}^{2}}$ the first factor of $2$makes the leading term into a perfect square. The additional ${{2}^{2}}$ factor avoids us having to divide, $3$ by $2$ and end up working with $\dfrac{1}{2}$ and $\dfrac{1}{4}$

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One cusec is equal to how many liters class 8 maths CBSE