Question

Solve the quadratic equation by completing the square.

$x^{2} +16x+54=0$

First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. If there is more than one solution, separate them with commas.

Answer 1

Answer:

$\sf x = -8 + \sqrt{10}$

$\sf x = -8 - \sqrt{10}$.

Step-by-step explanation:

To solve the quadratic equation $\sf x^2 + 16x + 54 = 0$ by completing the square, follow these steps:

$\sf x^2 + 16x + 54 = 0$

Move the constant term to the other side of the equation:

$\sf x^2 + 16x = -54$

Take half of the coefficient of $\sf x$ (which is 16), square it, and add it to both sides:

$\sf x^2 + 16x + \left(\dfrac{16}{2}\right)^2 = -54 + \left(\dfrac{16}{2}\right)^2$

$\sf x^2 + 16x + 64 = -54 + 64$

Factor the perfect square trinomial on the left side:

$\sf (x + 8)^2 = 10$

Take the square root of both sides:

$\sf x + 8 = \pm \sqrt{10}$

Solve for $\sf x$:

$\sf x = -8 \pm \sqrt{10}$

So, the solutions to the quadratic equation are:

$\sf x = -8 + \sqrt{10}$ and

$\sf x = -8 - \sqrt{10}$