Answer:
The solution of the equations are x = 30.33 and x = -0.33 .
Step-by-step explanation:
As given
x² – 30x - 10 = 0
As the general form of equation is written as
ax² + bx + c = 0
a = 1 , b = -30 ,c= -10
The discriminant form is defined as
[tex]x = \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
Put all the values in the discriment formula
[tex]x = \frac{-(-30)\pm\sqrt{(-30)^{2}-4\times 1\times -10}}{2}[/tex]
As
[tex]x = \frac{-(-30)+\sqrt{(-30)^{2}-4\times 1\times -10}}{2}[/tex]
[tex]x = \frac{-(-30)+\sqrt{900+40}}{2}[/tex]
[tex]x = \frac{(30)+\sqrt{940}}{2}[/tex]
[tex]x = \frac{(30)+\sqrt{940}}{2}[/tex]
[tex]\sqrt{940} = 30.66[/tex]
[tex]x = \frac{(30)+30.66}{2}[/tex]
[tex]x = \frac{60.66}{2}[/tex]
x = 30.33
As
[tex]x = \frac{-(-30)-\sqrt{900+40}}{2}[/tex]
[tex]x = \frac{(30)-\sqrt{940}}{2}[/tex]
[tex]x = \frac{(30)-\sqrt{940}}{2}[/tex]
[tex]\sqrt{940} = 30.66[/tex]
[tex]x = \frac{(30)-30.66}{2}[/tex]
[tex]x = \frac{-0.66}{2}[/tex]
x = -0.33
Therefore the solution of the equations are x = 30.33 and x = -0.33 .
