solve the equation and check the solution

Question

9w^2+8w+1=0.

Answer 1

9w ^2 + 8w + 1 = 0 is quadratic, use the Quadratic Formula to find the roots of the related quadratic equation.

w = [- b ± sqrt(b ^2 - 4ac)] / 2a.

Substitute b = 8, a = 9, and c = 1.

w = [-8 ± sqrt(8^2 - (4 * 9 * 1))] / 2 * 9

= [- 8 ± sqrt(64 - 36)] / 18

= [- 8 ± sqrt(28)] / 18

= [- 8 ± 2sqrt(7)] / 18

= [- 4 ± sqrt( 7)] / 9

= [- 4 ± 2.64] / 9

= [- 4 + 2.64] / 9 (or) [- 4 - 2.64] / 9

w = - 0.15 (or) - 0.73.

Sulution of the equation is w = - 0.15 (0r) - 0.73.

Check :

Substitute the w = - 0.15 in 9w ^2 + 8w + 1 = 0.

9(- 0.15)^2 + 8(- 0.15) + 1 = 0

9( 0.225) - 1.2 + 1 = 0

0.2 - 1.2 + 1 = 0

1.2 - 1.2 = 0

0 = 0.

The above statement is true, so w = - 0.15 is a solution of 9w ^2 + 8w + 1 = 0.

Substitute the w = - 0.73 in 9w ^2 + 8w + 1 = 0.

9(- 0.73)^2 + 8(- 0.73) + 1 = 0

4.8 - 5.8 + 1 = 0

5.8 - 5.8 = 0

0 = 0.

The above statement is true, so w = - 0.73 is a solution of 9w ^2 + 8w + 1 = 0.