Question

Solve by completion of square 2x2+x-4

Answer 1

2*2+x-4=0

4+x-4=0

x-4=-4

x=-4+4

x=0

Answer 2

SOLVING A QUADRATIC EQUATION USING COMPLETION OF SQUARE METHOD :-

$2 {x}^{2} + x - 4 = 0 \\ \\ \\ \implies {x}^{2} + \frac{ x}{2} - 2 = 0 \\ \\ \\ \implies {x}^{2} + \frac{x}{2} = 2 \\ \\ \\ \implies {x}^{2} + 2 \times \frac{x}{4} = 2 \\ \\ \\ \implies {x}^{2} + 2 \times x \times \frac{1}{4} = 2 \\ \\ \\ \implies {(x)}^{2} + 2 \times x \times \frac{1}{4} + { (\frac{1}{4}) }^{2} = 2 + { (\frac{1}{4}) }^{2} \\ \\ \\ \implies {(x + \frac{1}{4}) }^{2} = 2 + \frac{1}{16} \\ \\ \\ \implies {(x + \frac{1}{4}) }^{2} = \frac{33}{16} \\ \\ \\ \implies x + \frac{1}{4} = \frac{ \pm \sqrt{33} }{4} \\ \\ \\ \implies \boxed{x = \frac{ - 1 + \sqrt{33} }{4} \: or \: \frac{ - 1 - \sqrt{33} }{4} }$

STEPS INVOLVED :-

1. Divide coefficient of x^2 in both LHS and RHS.

2. Multiply and divide 2 with the term containing x .

3. Separate 2 , x and remaining fraction from the middle term.

4. Add square of middle term both the sides.

5. In LHS use (a+b)^2 identity in reverse.

6. Apply root on both the sides and find out the values of x .

7. As it is quadratic equation it must have two solution.

SHORT - CUT FORMULA :-

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \\ where \\ a = coefficient \: of \: {x}^{2} \\ b = coefficient \: of \: x \\ c = constant \: term$