Respuesta :
The solution of the equation is [tex]x=\frac{5-\sqrt{13}}{2},\:x=\frac{5+\sqrt{13}}{2}[/tex]
Explanation:
The given equation is [tex]-x^2+5x-3=0[/tex]
We need to determine the solution of the given equation.
The solution can be determined by finding the roots for the equation.
Let us use the quadratic formula to find the roots of the equation.
From the equation, we have,
[tex]a=-1,\:b=5,\:c=-3[/tex]
Let us substitute these values in the quadratic formula,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Thus, we have,
[tex]x=\frac{-5\pm \sqrt{5^2-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}[/tex]
Simplifying the terms, we have,
[tex]x=\frac{-5\pm \sqrt{25-12}}{-2}[/tex]
[tex]x=\frac{-5\pm \sqrt{13}}{-2}[/tex]
Thus, the values of x are [tex]x=\frac{-5 + \sqrt{13}}{-2}[/tex] and [tex]x=\frac{-5-\sqrt{13}}{-2}[/tex]
Simplifying the roots of the quadratic equation, we have,
[tex]x=\frac{-(5 - \sqrt{13})}{-2}[/tex] and [tex]x=\frac{-(5+\sqrt{13})}{-2}[/tex]
Cancelling the negative signs, we get,
[tex]x=\frac{5 - \sqrt{13}}{2}[/tex] and [tex]x=\frac{5+\sqrt{13}}{2}[/tex]
Thus, the solutions of the given equation are [tex]x=\frac{5 - \sqrt{13}}{2}[/tex] and [tex]x=\frac{5+\sqrt{13}}{2}[/tex]
