Respuesta :
So, this is too vague but I'll solve for both quadratic formula and find the discriminant.
Quadratic formula: x=5+√35 OR x=5−√35
Finding the discriminant: 141
Quadratic formula: x=5+√35 OR x=5−√35
Finding the discriminant: 141
Answer:
[tex]x_{1}=5+\sqrt{35}[/tex]
[tex]x_{2}=5-\sqrt{35}[/tex]
Step-by-step explanation:
the equation is
[tex]x^2-10x+25=35[/tex]
to solve we need to make the equation equal to zero, for that we substract 35 on each side:
[tex]x^2-10x+25-35=0\\x^2-10x-10=0[/tex]
we have now an equation in the general form: [tex]ax^2+bx+c=0[/tex]
where
[tex]a=1[/tex]
[tex]b=-10[/tex]
[tex]c=-10[/tex]
and we find the values for x with the general formula:
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
substituting known values
[tex]x=\frac{-(-10)+-\sqrt{(-10)^2-4(1)(-10)} }{2(1)}\\x=\frac{10+-\sqrt{100+40} }{2}\\x=\frac{10+-\sqrt{140} }{2}\\x=\frac{10+-\sqrt{4*35} }{2}\\x=\frac{10+-2\sqrt{35} }{2}\\x=5+-\sqrt{35}[/tex]
since we had a quadratic equation we will have 2 answers, one taking the positive sign and the other with the negative sign:
[tex]x_{1}=5+\sqrt{35}[/tex] ≈ 10.916
[tex]x_{2}=5-\sqrt{35}[/tex] ≈ -0.916
