(9x^2-7x+19)+(2x^2+9x-52)=

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Solution for (9x^2-7x+19)+(2x^2+9x-52)= equation:


Simplifying
(9x2 + -7x + 19) + (2x2 + 9x + -52) = 0

Reorder the terms:
(19 + -7x + 9x2) + (2x2 + 9x + -52) = 0

Remove parenthesis around (19 + -7x + 9x2)
19 + -7x + 9x2 + (2x2 + 9x + -52) = 0

Reorder the terms:
19 + -7x + 9x2 + (-52 + 9x + 2x2) = 0

Remove parenthesis around (-52 + 9x + 2x2)
19 + -7x + 9x2 + -52 + 9x + 2x2 = 0

Reorder the terms:
19 + -52 + -7x + 9x + 9x2 + 2x2 = 0

Combine like terms: 19 + -52 = -33
-33 + -7x + 9x + 9x2 + 2x2 = 0

Combine like terms: -7x + 9x = 2x
-33 + 2x + 9x2 + 2x2 = 0

Combine like terms: 9x2 + 2x2 = 11x2
-33 + 2x + 11x2 = 0

Solving
-33 + 2x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-3 + 0.1818181818x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 0.1818181818x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 0.1818181818x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 0.1818181818x + x2 = 0 + 3
0.1818181818x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
0.1818181818x + x2 = 3

The x term is 0.1818181818x.  Take half its coefficient (0.0909090909).
Square it (0.008264462808) and add it to both sides.

Add '0.008264462808' to each side of the equation.
0.1818181818x + 0.008264462808 + x2 = 3 + 0.008264462808

Reorder the terms:
0.008264462808 + 0.1818181818x + x2 = 3 + 0.008264462808

Combine like terms: 3 + 0.008264462808 = 3.008264462808
0.008264462808 + 0.1818181818x + x2 = 3.008264462808

Factor a perfect square on the left side:
(x + 0.0909090909)(x + 0.0909090909) = 3.008264462808

Calculate the square root of the right side: 1.734434912

Break this problem into two subproblems by setting 
(x + 0.0909090909) equal to 1.734434912 and -1.734434912.

Subproblem 1

x + 0.0909090909 = 1.734434912 Simplifying x + 0.0909090909 = 1.734434912 Reorder the terms: 0.0909090909 + x = 1.734434912 Solving 0.0909090909 + x = 1.734434912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = 1.734434912 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 1.734434912 + -0.0909090909 x = 1.734434912 + -0.0909090909 Combine like terms: 1.734434912 + -0.0909090909 = 1.6435258211 x = 1.6435258211 Simplifying x = 1.6435258211

Subproblem 2

x + 0.0909090909 = -1.734434912 Simplifying x + 0.0909090909 = -1.734434912 Reorder the terms: 0.0909090909 + x = -1.734434912 Solving 0.0909090909 + x = -1.734434912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = -1.734434912 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -1.734434912 + -0.0909090909 x = -1.734434912 + -0.0909090909 Combine like terms: -1.734434912 + -0.0909090909 = -1.8253440029 x = -1.8253440029 Simplifying x = -1.8253440029

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.6435258211, -1.8253440029}

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