Answer:
x=1.53
x=6.53
Step-by-step explanation:
The first thing to do is to leave the equation equal to zero expressed.
\(x^{2} =-5x+8\\x^{2}+5x-8=0\)
Next, being a second degree equation, we can use the general formula to find the solutions. This equation is as follows:
\(x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}\)
Where a is the coefficient of the quadratic term, b the coefficient of the linear term and c the coefficient of the value without variable.
In this case: a=1, b=5, c=-8
Replacing in the ecuation
\(x_{1} =\frac{-5+\sqrt{(5^{2})-4(1)(-8) } }{2(1)}\)
\(x_{1} =\frac{-5+\sqrt{25+32} }{2}= \frac{-5+\sqrt{57} }{2} = \frac{-5+7.54}{2} =\frac{2.54}{2} =1.27\)
Now
\(x_{2} =\frac{-5-\sqrt{(5^{2})-4(1)(-8)} }{2}=\frac{-5-\sqrt{25+32} }{2}= \frac{-5-\sqrt{57} }{2} = \frac{-5-7.54}{2} =\frac{12.54}{2} =6.27\)
So, both solution:
x=1.53
x=6.53
