Find the zeroes of the function and write in a+bi form. -(x+1)^2-4=0

x = 2  +  √-16 [ (-2)⁻¹]

See steps below.

Step-by-step explanation:

Finding the zeroes of a function simply means solving for the unknown variable (in this case "x") when the function is equated to zero.

The function here is  

Start by opening the bracket. Ignore the minus sign. It will be reintroduced at the end of this step.

(x + 1)(x + 1)   = x² + x + x + 1    = x² + 2x + 1

Reintroduce the minus sign. Don't forget to put the result above back in a bracket.

- (x² + 2x + 1)  = -x² -2x -1

Place the expression back in the equation and solve. Make sure to put it back in the position where it was.

-x² - 2x - 1 - 4 = 0

Simplify the non-algebraic terms.

-x² - 2x - 5 = 0

Use Quadratic Formula to solve for x.

Quadratic formula: x =  -b ± √(b² - 4ac)

                                              2a

a = the coefficient of x² = -1

b = the coefficient of x  = -2

c = the unit term            = -5

So   x = -(-2)  ± √ [(-2)² - 4(-1 x -5)]

                       2(-1)

x = 2 + √-16                    or x = 2 - √-16

         -2                                          -2

This is where the evaluation ends, since the square root of minus sixteen cannot be evaluated. x hence is equal to a complex number. The above are the two values for x.

Next step is to put it in "a + bi" form.

x = 2  +  √-16  ÷  -2     =  2  +  √-16  x (-2)⁻¹

So   x = 2  +  √-16 [ (-2)⁻¹]

where

a is 2;

b is √-16

i is [(-2)⁻¹]

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .