enter the correct answer in the box. solve the equation x² - 16x + 54 = 0 by completing the square. fill in…

Explanation:

Step1: Rewrite the equation

Given $x^{2}-16x + 54=0$. Move the constant term to the right - hand side: $x^{2}-16x=-54$.

Step2: Complete the square on the left - hand side

For the quadratic expression $x^{2}-16x$, the coefficient of $x$ is $-16$. Half of it is $\frac{-16}{2}=-8$, and its square is $(-8)^{2} = 64$. Add 64 to both sides of the equation: $x^{2}-16x + 64=-54 + 64$.

Step3: Factor the left - hand side and simplify the right - hand side

The left - hand side factors to $(x - 8)^{2}$, and the right - hand side simplifies to 10. So, $(x - 8)^{2}=10$.

Step4: Solve for $x$

Take the square root of both sides: $x-8=\pm\sqrt{10}$. Then $x = 8\pm\sqrt{10}$.

Answer:

$a = 8$, $b = 10$