9x^2+35x+32=0

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Solution for 9x^2+35x+32=0 equation:


Simplifying
9x2 + 35x + 32 = 0

Reorder the terms:
32 + 35x + 9x2 = 0

Solving
32 + 35x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
3.555555556 + 3.888888889x + x2 = 0

Move the constant term to the right:

Add '-3.555555556' to each side of the equation.
3.555555556 + 3.888888889x + -3.555555556 + x2 = 0 + -3.555555556

Reorder the terms:
3.555555556 + -3.555555556 + 3.888888889x + x2 = 0 + -3.555555556

Combine like terms: 3.555555556 + -3.555555556 = 0.000000000
0.000000000 + 3.888888889x + x2 = 0 + -3.555555556
3.888888889x + x2 = 0 + -3.555555556

Combine like terms: 0 + -3.555555556 = -3.555555556
3.888888889x + x2 = -3.555555556

The x term is 3.888888889x.  Take half its coefficient (1.944444445).
Square it (3.780864200) and add it to both sides.

Add '3.780864200' to each side of the equation.
3.888888889x + 3.780864200 + x2 = -3.555555556 + 3.780864200

Reorder the terms:
3.780864200 + 3.888888889x + x2 = -3.555555556 + 3.780864200

Combine like terms: -3.555555556 + 3.780864200 = 0.225308644
3.780864200 + 3.888888889x + x2 = 0.225308644

Factor a perfect square on the left side:
(x + 1.944444445)(x + 1.944444445) = 0.225308644

Calculate the square root of the right side: 0.474666877

Break this problem into two subproblems by setting 
(x + 1.944444445) equal to 0.474666877 and -0.474666877.

Subproblem 1

x + 1.944444445 = 0.474666877 Simplifying x + 1.944444445 = 0.474666877 Reorder the terms: 1.944444445 + x = 0.474666877 Solving 1.944444445 + x = 0.474666877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.944444445' to each side of the equation. 1.944444445 + -1.944444445 + x = 0.474666877 + -1.944444445 Combine like terms: 1.944444445 + -1.944444445 = 0.000000000 0.000000000 + x = 0.474666877 + -1.944444445 x = 0.474666877 + -1.944444445 Combine like terms: 0.474666877 + -1.944444445 = -1.469777568 x = -1.469777568 Simplifying x = -1.469777568

Subproblem 2

x + 1.944444445 = -0.474666877 Simplifying x + 1.944444445 = -0.474666877 Reorder the terms: 1.944444445 + x = -0.474666877 Solving 1.944444445 + x = -0.474666877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.944444445' to each side of the equation. 1.944444445 + -1.944444445 + x = -0.474666877 + -1.944444445 Combine like terms: 1.944444445 + -1.944444445 = 0.000000000 0.000000000 + x = -0.474666877 + -1.944444445 x = -0.474666877 + -1.944444445 Combine like terms: -0.474666877 + -1.944444445 = -2.419111322 x = -2.419111322 Simplifying x = -2.419111322

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.469777568, -2.419111322}

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