9x^2+45x+38=0

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Solution for 9x^2+45x+38=0 equation:


Simplifying
9x2 + 45x + 38 = 0

Reorder the terms:
38 + 45x + 9x2 = 0

Solving
38 + 45x + 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'.
4.222222222 + 5x + x2 = 0

Move the constant term to the right:

Add '-4.222222222' to each side of the equation.
4.222222222 + 5x + -4.222222222 + x2 = 0 + -4.222222222

Reorder the terms:
4.222222222 + -4.222222222 + 5x + x2 = 0 + -4.222222222

Combine like terms: 4.222222222 + -4.222222222 = 0.000000000
0.000000000 + 5x + x2 = 0 + -4.222222222
5x + x2 = 0 + -4.222222222

Combine like terms: 0 + -4.222222222 = -4.222222222
5x + x2 = -4.222222222

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -4.222222222 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -4.222222222 + 6.25

Combine like terms: -4.222222222 + 6.25 = 2.027777778
6.25 + 5x + x2 = 2.027777778

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 2.027777778

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.424000624 and -1.424000624.

Subproblem 1

x + 2.5 = 1.424000624 Simplifying x + 2.5 = 1.424000624 Reorder the terms: 2.5 + x = 1.424000624 Solving 2.5 + x = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.424000624 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.424000624 + -2.5 x = 1.424000624 + -2.5 Combine like terms: 1.424000624 + -2.5 = -1.075999376 x = -1.075999376 Simplifying x = -1.075999376

Subproblem 2

x + 2.5 = -1.424000624 Simplifying x + 2.5 = -1.424000624 Reorder the terms: 2.5 + x = -1.424000624 Solving 2.5 + x = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.424000624 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.424000624 + -2.5 x = -1.424000624 + -2.5 Combine like terms: -1.424000624 + -2.5 = -3.924000624 x = -3.924000624 Simplifying x = -3.924000624

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.075999376, -3.924000624}

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