Question

solution of quadratic equation by completing the square 4 x square + 8 x + 4 is equal to zerosolution of quadratic equation by completing the square 4 x square + 8 x + 4 is equal to zero ​

Answer 1

To FIND :- Solution of the equation by completing square method.

$4 {x}^{2} + 8x + 4 = 0 \\ \\ \implies {x}^{2} + 2x + 2 = 0 \\ \\ \implies {x}^{2} + 2 \times \frac{2x}{2} + 2 = 0 \\ \\ \implies {x}^{2} + 2 \times \frac{2}{2} \times x = - 2 \\ \\ \implies {x}^{2} + 2x + 1 = - 2 + 1 \\ \\ \implies {(x + 1)}^{2} = - 1 \\ \\ \implies x + 1 = \pm \sqrt{ - 1} \\ \\ \implies x = - 1 \pm \sqrt{1} \\ \\ \implies x = \sqrt{1} - 1 \: or \: - \sqrt{1} - 1 \\ \\ \implies x = 0 \: or - 2$

STEPS FOR COMPLETING SQUARE METHOD :-

1. Divide coefficient of x^4 in both LHS and RHS.

2.Multiply and divide coefficient of x in the x term.

3. Add the square of x term in both the sides.

4.Solve for x.