(9x^2-5x-27)+(4x^2+8x)=

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Solution for (9x^2-5x-27)+(4x^2+8x)= equation:


Simplifying
(9x2 + -5x + -27) + (4x2 + 8x) = 0

Reorder the terms:
(-27 + -5x + 9x2) + (4x2 + 8x) = 0

Remove parenthesis around (-27 + -5x + 9x2)
-27 + -5x + 9x2 + (4x2 + 8x) = 0

Reorder the terms:
-27 + -5x + 9x2 + (8x + 4x2) = 0

Remove parenthesis around (8x + 4x2)
-27 + -5x + 9x2 + 8x + 4x2 = 0

Reorder the terms:
-27 + -5x + 8x + 9x2 + 4x2 = 0

Combine like terms: -5x + 8x = 3x
-27 + 3x + 9x2 + 4x2 = 0

Combine like terms: 9x2 + 4x2 = 13x2
-27 + 3x + 13x2 = 0

Solving
-27 + 3x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-2.076923077 + 0.2307692308x + x2 = 0

Move the constant term to the right:

Add '2.076923077' to each side of the equation.
-2.076923077 + 0.2307692308x + 2.076923077 + x2 = 0 + 2.076923077

Reorder the terms:
-2.076923077 + 2.076923077 + 0.2307692308x + x2 = 0 + 2.076923077

Combine like terms: -2.076923077 + 2.076923077 = 0.000000000
0.000000000 + 0.2307692308x + x2 = 0 + 2.076923077
0.2307692308x + x2 = 0 + 2.076923077

Combine like terms: 0 + 2.076923077 = 2.076923077
0.2307692308x + x2 = 2.076923077

The x term is 0.2307692308x.  Take half its coefficient (0.1153846154).
Square it (0.01331360947) and add it to both sides.

Add '0.01331360947' to each side of the equation.
0.2307692308x + 0.01331360947 + x2 = 2.076923077 + 0.01331360947

Reorder the terms:
0.01331360947 + 0.2307692308x + x2 = 2.076923077 + 0.01331360947

Combine like terms: 2.076923077 + 0.01331360947 = 2.09023668647
0.01331360947 + 0.2307692308x + x2 = 2.09023668647

Factor a perfect square on the left side:
(x + 0.1153846154)(x + 0.1153846154) = 2.09023668647

Calculate the square root of the right side: 1.445765087

Break this problem into two subproblems by setting 
(x + 0.1153846154) equal to 1.445765087 and -1.445765087.

Subproblem 1

x + 0.1153846154 = 1.445765087 Simplifying x + 0.1153846154 = 1.445765087 Reorder the terms: 0.1153846154 + x = 1.445765087 Solving 0.1153846154 + x = 1.445765087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = 1.445765087 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = 1.445765087 + -0.1153846154 x = 1.445765087 + -0.1153846154 Combine like terms: 1.445765087 + -0.1153846154 = 1.3303804716 x = 1.3303804716 Simplifying x = 1.3303804716

Subproblem 2

x + 0.1153846154 = -1.445765087 Simplifying x + 0.1153846154 = -1.445765087 Reorder the terms: 0.1153846154 + x = -1.445765087 Solving 0.1153846154 + x = -1.445765087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = -1.445765087 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = -1.445765087 + -0.1153846154 x = -1.445765087 + -0.1153846154 Combine like terms: -1.445765087 + -0.1153846154 = -1.5611497024 x = -1.5611497024 Simplifying x = -1.5611497024

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.3303804716, -1.5611497024}

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