After completing the square what are the solutions to the quadratic equation below
x²-5x-6=3

x = 5/2 + sqrt(61)/2 or x = 5/2 - sqrt(61)/2

Step-by-step explanation:

Solve for x over the real numbers:

x^2 - 5 x - 6 = 3

Hint: | Solve the quadratic equation by completing the square.

Add 6 to both sides:

x^2 - 5 x = 9

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 25/4 to both sides:

x^2 - 5 x + 25/4 = 61/4

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 5/2)^2 = 61/4

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 5/2 = sqrt(61)/2 or x - 5/2 = -sqrt(61)/2

Hint: | Look at the first equation: Solve for x.

Add 5/2 to both sides:

x = 5/2 + sqrt(61)/2 or x - 5/2 = -sqrt(61)/2

Hint: | Look at the second equation: Solve for x.

Add 5/2 to both sides:

x = 5/2 + sqrt(61)/2 or x = 5/2 - sqrt(61)/2

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!