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

line or a linear equation graph

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!