Question

${2}x^{2} - 2x + \frac{1}{2} = 0$
by factorization method



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Answer 1

Answer:

       x = 1 / 2

Step-by-step explanation:

2x² - 2x + 1/2 = 0

4x² - 4x + 1 = 0

4x² - 2x - 2x + 1 = 0

2x(2x - 1) - 1(2x - 1) = 0

(2x - 1) (2x - 1) = 0

2x - 1 = 0

x = 1 / 2

Answer 2

To Find:

• The value of x by factorisation method.

Given quadratic equation.

ㅤ↠ㅤ2x² - 2x + 1/2 = 0

Splitting the mid-term.

ㅤ↠ㅤ2x² - (1 + 1)x + 1/2 = 0

ㅤ↠ㅤ2x² - x - x + 1/2 = 0

Here x can be also written as 2x/2.

ㅤ↠ㅤ2x² - 2x/2 - x + 1/2 = 0

Taking 2x and - 1 common.

ㅤ↠ㅤ2x(x - 1/2) - 1(x - 1/2) = 0

ㅤ↠ㅤ(2x - 1) (x - 1/2) = 0

Here,

ㅤ↠ㅤ(2x - 1) = 0 or (x - 1/2) = 0

ㅤ↠ㅤ2x = 1 or x = 1/2

ㅤ↠ㅤx = 1/2 or x = 1/2

Hence,

• The value of x = 1/2.

Verification:

• In equation 2x² - 2x + 1/2 = 0

L.H.S: 2x² - 2x + 1/2

Putting the value x = 1/2.

ㅤ=ㅤ2(1/2)² - 2(1/2) + 1/2

ㅤ=ㅤ2(1/4) - 2/2 + 1/2

ㅤ=ㅤ2/4 - 1 + 1/2

ㅤ=ㅤ1/2 - 1 + 1/2

ㅤ=ㅤ0

ㅤ=ㅤR.H.S

Verified.