2x(9-5x)-(-4-6x^2)=

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Solution for 2x(9-5x)-(-4-6x^2)= equation: 


Simplifying
2x(9 + -5x) + -1(-4 + -6x2) = 0
(9 * 2x + -5x * 2x) + -1(-4 + -6x2) = 0
(18x + -10x2) + -1(-4 + -6x2) = 0
18x + -10x2 + (-4 * -1 + -6x2 * -1) = 0
18x + -10x2 + (4 + 6x2) = 0

Reorder the terms:
4 + 18x + -10x2 + 6x2 = 0

Combine like terms: -10x2 + 6x2 = -4x2
4 + 18x + -4x2 = 0

Solving
4 + 18x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 9x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 9x + -2x2)' equal to zero and attempt to solve:

Simplifying
2 + 9x + -2x2 = 0

Solving
2 + 9x + -2x2 = 0

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

Divide each side by '-2'.
-1 + -4.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.5x + x2 = 0 + 1
-4.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.5x + x2 = 1

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 1 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 1 + 5.0625

Combine like terms: 1 + 5.0625 = 6.0625
5.0625 + -4.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.46221445 and -2.46221445.


Subproblem 1
x + -2.25 = 2.46221445

Simplifying
x + -2.25 = 2.46221445

Reorder the terms:
-2.25 + x = 2.46221445

Solving
-2.25 + x = 2.46221445

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.46221445 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.46221445 + 2.25
x = 2.46221445 + 2.25

Combine like terms: 2.46221445 + 2.25 = 4.71221445
x = 4.71221445

Simplifying
x = 4.71221445


Subproblem 2
x + -2.25 = -2.46221445

Simplifying
x + -2.25 = -2.46221445

Reorder the terms:
-2.25 + x = -2.46221445

Solving
-2.25 + x = -2.46221445

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.46221445 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.46221445 + 2.25
x = -2.46221445 + 2.25

Combine like terms: -2.46221445 + 2.25 = -0.21221445
x = -0.21221445

Simplifying
x = -0.21221445


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.71221445, -0.21221445}
Solution
x = {4.71221445, -0.21221445}

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