Question

Solve the equation following quadratic equation by method of completing the square 2 x square - 5 x + 3 = 0

Answer 1

Question

Solve the equation following quadratic equation by method of completing the square 2 x² - 5 x + 3 = 0.

Solution

Given :-

• Equation, 2x² - 5x + 3 = 0

Find :-

• Solution of this equation by completing square method

Explanation

Complete Square Method

Steps(1).

• First keep constant part in R.H.S.

So,

==> 2x² - 5x = -3

Steps(2).

• Keep identity coefficient of x² , for this divided by 2 both side

==> (2x² - 5x)/2 = -3/2

==> x² - 5x/2 = -3/2

==> x² - 2 * x * 5/4 = -3/2

Steps(3).

• Add 25/16 both side

==> x² - 2 * x * 5/4 + 25/16 = -3/2 + 25/16

==> x² - 2 * x * 5/4 + (5/4)² = (-3*8+25)/16

Using Formula

• (a-b)² = a² - 2ab + b²

==> (x - 5/4)² = (-24+25)/16

==> (x - 5/4 )² = 1/16

==> (x - 5/4) = √(1/16)

==> x = ± 1/4 + 5/4

First take ( +ve) Sign

==> x = 1/4 + 5/4

==> x = (1+5)/4

==> x = 6/4

==> x = 3/2

Now, take (-ve) Sign

==> x = -1/4 + 5/4

==> x = (-1+5)/4

==> x = 4/4

==> x = 1

Hence

• Value of x be = 3/2 & 1

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