orWatch a videoSolve by completing the square.z2 + 8z = 47Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.z = or z =

To solve the equation z^2 + 8z = 47 by completing the square, follow these steps:

Step 1: Rearrange the equation so that the z^2 and z terms are on one side of the equation and the constant is on the other side. The equation is already in this form.

Step 2: To complete the square, we need to add the square of half the coefficient of z to both sides of the equation. Half of 8 is 4, and 4^2 is 16. So, we add 16 to both sides of the equation:

z^2 + 8z + 16 = 47 + 16 z^2 + 8z + 16 = 63

Step 3: The left side of the equation can now be written as a perfect square:

(z + 4)^2 = 63

Step 4: Take the square root of both sides of the equation. Remember to consider both the positive and negative roots:

z + 4 = sqrt(63) or z + 4 = -sqrt(63)

Step 5: Solve for z by subtracting 4 from both sides of the equation:

z = sqrt(63) - 4 or z = -sqrt(63) - 4

So, the solutions to the equation z^2 + 8z = 47 are z = sqrt(63) - 4 and z = -sqrt(63) - 4.