(x+5)(3-x)=33

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Solution for (x+5)(3-x)=33 equation: 


Simplifying
(x + 5)(3 + -1x) = 33

Reorder the terms:
(5 + x)(3 + -1x) = 33

Multiply (5 + x) * (3 + -1x)
(5(3 + -1x) + x(3 + -1x)) = 33
((3 * 5 + -1x * 5) + x(3 + -1x)) = 33
((15 + -5x) + x(3 + -1x)) = 33
(15 + -5x + (3 * x + -1x * x)) = 33
(15 + -5x + (3x + -1x2)) = 33

Combine like terms: -5x + 3x = -2x
(15 + -2x + -1x2) = 33

Solving
15 + -2x + -1x2 = 33

Solving for variable 'x'.

Reorder the terms:
15 + -33 + -2x + -1x2 = 33 + -33

Combine like terms: 15 + -33 = -18
-18 + -2x + -1x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-18 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 2x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(18 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
18 + 2x + x2 = 0

Solving
18 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 2x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 2x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 2x + x2 = 0 + -18
2x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
2x + x2 = -18

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -18 + 1

Reorder the terms:
1 + 2x + x2 = -18 + 1

Combine like terms: -18 + 1 = -17
1 + 2x + x2 = -17

Factor a perfect square on the left side:
(x + 1)(x + 1) = -17

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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