Hey!
The first step to solving this equation would be to subtract 5 from both sides of the equation.
Original Equation :
[tex] x^{2} [/tex] - 8x + 16 = 5
New Equation {Added Subtract 5 to Both Sides} :
[tex] x^{2} [/tex] - 8x + 16 - 5 = 5 - 5
Now we solve our new equation.
Old Equation :
[tex] x^{2} [/tex] - 8x + 16 - 5 = 5 - 5
Solution {Old Equation Solved} :
[tex] x^{2} [/tex] - 8x + 11 = 0
The next step would be to solve with the quadratic formula.
Quadratic Equation ( 1 ) :
[tex]x = \frac{-(-8) + \sqrt{(-8)^{2} -4 * 1 * 11 } }{2*1} [/tex]
Quadratic Equation ( 1 ) {Solved} :
4 + [tex] \sqrt{5} [/tex]
Quadratic Equation ( 2 ) :
[tex]x = \frac{-(-8) - \sqrt{(-8)^{2}-4 *1*11 } }{2*1} [/tex]
Quadratic Equation ( 2 ) {Solved} :
4 - [tex] \sqrt{5} [/tex]
So, our final solutions for the equation [tex] x^{2} [/tex] - 8x + 16 = 5 are...
x = 4 + [tex] \sqrt{5} [/tex]
and
x = 4 - [tex] \sqrt{5} [/tex]
Hope this helps!
- Lindsey Frazier ♥
