Answer:
x = [ -b +- sqr root (b^2 - 4ac)] / 2a
a = 1
b = -5
c = -2
x = [- - 5 +- sqr root (-5^2 -4 * 1 * -2)] / 2 * 1
x = [5 +- sqr root (25 + 8)] / 2
x1 = 5.3723
x2 =-0.37228
Step-by-step explanation:
Exact solution for the give quadratic equation are
[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]
Quadratic equation of the form [tex]ax^2+bx+c=0[/tex]
For any quadratic equation we get two values for x. we can find the values for x by applying quadratic formula .
Quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Given equation is [tex]x^2-5x-2=0[/tex]
The value of a=1, b= -5 and c=-2
Substitute all the values in the formula.
To find out exact solutions , we need to simplify the final answer.
Exact solutions are without any decimals.
[tex]x=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\pm \sqrt{33}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\p+ \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5+\sqrt{33}}{2}\\\\x=\frac{-\left(-5\right)- \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5-\sqrt{33}}{2}\\[/tex]
Exact solutions are
[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]
Learn more information about 'Quadratic formula ' here
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