Question

X^2-8x+16=5 what are the solutions?

Answer 1

Hey!


The first step to solving this equation would be to subtract 5 from both sides of the equation.

Original Equation :
$x^{2}$ - 8x + 16 = 5

New Equation {Added Subtract 5 to Both Sides} :
$x^{2}$ - 8x + 16 - 5 = 5 - 5

Now we solve our new equation.

Old Equation :
$x^{2}$ - 8x + 16 - 5 = 5 - 5

Solution {Old Equation Solved} :
$x^{2}$ - 8x + 11 = 0

The next step would be to solve with the quadratic formula.

Quadratic Equation ( 1 ) :
$x = \frac{-(-8) + \sqrt{(-8)^{2} -4 * 1 * 11 } }{2*1}$

Quadratic Equation ( 1 ) {Solved} :
4 + $\sqrt{5}$

Quadratic Equation ( 2 ) :
$x = \frac{-(-8) - \sqrt{(-8)^{2}-4 *1*11 } }{2*1}$

Quadratic Equation ( 2 ) {Solved} :
4 - $\sqrt{5}$

So, our final solutions for the equation $x^{2}$ - 8x + 16 = 5 are...

x = 4 + $\sqrt{5}$

and 

x = 4 - $\sqrt{5}$

Hope this helps!


- Lindsey Frazier ♥