7(3x-5)-2x(x+11)=0

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Solution for 7(3x-5)-2x(x+11)=0 equation: 


Simplifying
7(3x + -5) + -2x(x + 11) = 0

Reorder the terms:
7(-5 + 3x) + -2x(x + 11) = 0
(-5 * 7 + 3x * 7) + -2x(x + 11) = 0
(-35 + 21x) + -2x(x + 11) = 0

Reorder the terms:
-35 + 21x + -2x(11 + x) = 0
-35 + 21x + (11 * -2x + x * -2x) = 0
-35 + 21x + (-22x + -2x2) = 0

Combine like terms: 21x + -22x = -1x
-35 + -1x + -2x2 = 0

Solving
-35 + -1x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(35 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
35 + x + 2x2 = 0

Solving
35 + x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
17.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-17.5' to each side of the equation.
17.5 + 0.5x + -17.5 + x2 = 0 + -17.5

Reorder the terms:
17.5 + -17.5 + 0.5x + x2 = 0 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + 0.5x + x2 = 0 + -17.5
0.5x + x2 = 0 + -17.5

Combine like terms: 0 + -17.5 = -17.5
0.5x + x2 = -17.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = -17.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -17.5 + 0.25

Combine like terms: -17.5 + 0.25 = -17.25
0.25 + 0.5x + x2 = -17.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -17.25

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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