Solve each of the following equation by using the method of completing the square:
$2 x^{2} + 5 x - 3 = 0$ ?

Open in App

Solution

We will use the difference of squares identity, which can be written:
$a^{2} - b^{2} = (a - b) (a + b)$ First,

to reduce the amount of arithmetic involving fractions, first multiply through by $2^{3} = 8$ toget:

$0 = {16 x}^{2} + 40 x - 24$

$= {4 x}^{2} + 2 (5) (4 x) - 24$

$= {(4 x + 5)}^{2} - 25 - 24$

$= {(4 x + 5)}^{2} - 7^{2}$
$= ((4 x + 5) - 7) ((4 x + 5) + 7)$

$= (4 x - 2) (4 x + 12)$

$= (2 (2 x - 1) 2 (2 x + 6))$

$= 4 (2 x - 1) (2 x + 6)$ Hence

: $x = \frac{1}{2}$ or $x = - 3$

Suggest Corrections

Similar questions

2 x^{2} + 5 x - 3 = 0

2 x^{2} - 5 x + 3 = 0

\sqrt{2} x^{2} - 3 x - 2 \sqrt{2} = 0

2 x^{2} + 5 x - 3 = 0

Solve the following equation using completing the square method.

$2 x^{2} - x + \frac{1}{8} = 0$

Join BYJU'S Learning Program