Answer
The equation has no real solution.
Work Step by Step
The given equation is
$\Rightarrow x^2=2x-5$
The coefficient of the $x^2-$ term is $1$, and the coefficient of the $x-$ term is an even number. So, solve by completing the square.
$\Rightarrow x^2=2x-5$
Subtract $2x$ from each side.
$\Rightarrow x^2-2x=2x-5-2x$
Simplify.
$\Rightarrow x^2-2x=-5$
Find the value of $(\frac{b}{2})^2$.
Substitute $-2$ for $b$.
$=(\frac{-2}{2})^2$
Simplify.
$=(-1)^2$
$=1$
Add $1$ to each side of the equation.
$\Rightarrow x^2-2x+1=-5+1$
Simplify.
$\Rightarrow x^2-2x+1=-4$
Write the left side as the square of a binomial.
$\Rightarrow (x-1)^2=-4$
Square root of a negative number is not a real number.
Hence, the equation has no real solution.
