enter the correct answer in the box. solve the equation $x^{2}-16x + 54 = 0$ by completing the square. fill…

enter the correct answer in the box. solve the equation $x^{2}-16x + 54 = 0$ by completing the square. fill in the values of a and b to complete the solutions. $x=a-sqrt{b}$ $x=a+sqrt{b}$

enter the correct answer in the box. solve the equation $x^{2}-16x + 54 = 0$ by completing the square. fill in the values of a and b to complete the solutions. $x=a-sqrt{b}$ $x=a+sqrt{b}$

Answer

Explanation:

Step1: Rewrite the equation for completing the square

For the quadratic equation (x^{2}-16x + 54=0), the coefficient of (x) is (- 16). Half of it is (\frac{-16}{2}=-8), and ((-8)^{2}=64). We rewrite the left - hand side as (x^{2}-16x+64 - 64 + 54=0), which is ((x - 8)^{2}-10=0).

Step2: Solve for (x)

Add 10 to both sides of the equation ((x - 8)^{2}-10=0) to get ((x - 8)^{2}=10). Then take the square root of both sides: (x-8=\pm\sqrt{10}). Finally, solve for (x): (x = 8\pm\sqrt{10}).

Answer:

(a = 8), (b = 10)