Respuesta :
Answer:
The solutions for the equations are x = 0.1644 and x = -12.1644
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]x^{2} + 12x - 2 = 0[/tex]
So
[tex]a = 1, b = 12, c = -2[/tex]
[tex]\bigtriangleup = 12^{2} - 4*1*(-2) = 152[/tex]
[tex]x_{1} = \frac{-12 + \sqrt{152}}{2} = 0.1644[/tex]
[tex]x_{2} = \frac{-12 - \sqrt{152}}{2} = -12.1644[/tex]
The solutions for the equations are x = 0.1644 and x = -12.1644
