Respuesta :
Answer:
5) [tex] x_1 = \frac{1+ \sqrt{95}}{2}[/tex]
[tex] x_2 = \frac{1- \sqrt{95}}{2}[/tex]
6) [tex] x_1=0[/tex]
[tex] x_2 = -\frac{1}{7}[/tex]
7) So for this case we have just one solution [tex] X=7[/tex]
8) [tex] d_1 = \frac{-5+\sqrt{121}}{4}=\frac{3}{2}[/tex]
[tex] d_2 = \frac{-5-\sqrt{121}}{4}= -4[/tex]
Step-by-step explanation:
5. x^2 − 1x + 19 = −5
For this case we can rewrite the expression like this:
[tex] x^2 - x + 24=0[/tex]
And then we can use the quadratic formula given by:
[tex] x= \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And for this case a= 1, b = -1 , c = 24, and replacing we got:
[tex] x= \frac{-(-1) \pm \sqrt{(-1)^2 -4(1)(24)}}{2(1)}[/tex]
[tex] x_1 = \frac{1+ \sqrt{95}}{2}[/tex]
[tex] x_2 = \frac{1- \sqrt{95}}{2}[/tex]
6. 7x^2 + x = 0
For this case we can take common factor first like this:
[tex x (7x +1) = 0[/tex]
So then [tex] x=0[/tex] or [tex] 7x+1=0[/tex] and we got that:
[tex] x = -\frac{1}{7}[/tex]
7. 7x^2 − 14x = −7
We can rewrite the expression like this:
[tex] 7x^2 -14x +7 = 0[/tex]
And then we can use the quadratic formula given by:
[tex] x= \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And for this case a= 7, b = -14 , c = 7, and replacing we got:
[tex] x= \frac{-(-14) \pm \sqrt{(-14)^2 -4(7)(7)}}{2(7)}[/tex]
[tex] x_1 = \frac{14+0}{14}=1[/tex]
[tex] x_2 = \frac{14-0}{14}= 1[/tex]
So for this case we have just one solution [tex] X=7[/tex]
8. 2d^2 + 5d − 12 = 0
We can use the quadratic formula given by:
[tex] d= \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
And for this case a= 2, b = 5 , c = -12, and replacing we got:
[tex] d= \frac{-(5) \pm \sqrt{(5)^2 -4(2)(-12)}}{2(2)}[/tex]
[tex] d_1 = \frac{-5+\sqrt{121}}{4}=\frac{3}{2}[/tex]
[tex] d_2 = \frac{-5-\sqrt{121}}{4}= -4[/tex]
