(5x*x)+9x+2=

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Solution for (5x*x)+9x+2= equation:


Simplifying
(5x * x) + 9x + 2 = 0

Multiply x * x
(5x2) + 9x + 2 = 0

Reorder the terms:
2 + 9x + (5x2) = 0

Solving
2 + 9x + (5x2) = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.4 + 1.8x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 1.8x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 1.8x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 1.8x + x2 = 0 + -0.4
1.8x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
1.8x + x2 = -0.4

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = -0.4 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = -0.4 + 0.81

Combine like terms: -0.4 + 0.81 = 0.41
0.81 + 1.8x + x2 = 0.41

Factor a perfect square on the left side:
((x) + 0.9)((x) + 0.9) = 0.41

Calculate the square root of the right side: 0.640312424

Break this problem into two subproblems by setting 
((x) + 0.9) equal to 0.640312424 and -0.640312424.

Subproblem 1

(x) + 0.9 = 0.640312424 Simplifying (x) + 0.9 = 0.640312424 x + 0.9 = 0.640312424 Reorder the terms: 0.9 + x = 0.640312424 Solving 0.9 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.640312424 + -0.9 x = 0.640312424 + -0.9 Combine like terms: 0.640312424 + -0.9 = -0.259687576 x = -0.259687576 Simplifying x = -0.259687576

Subproblem 2

(x) + 0.9 = -0.640312424 Simplifying (x) + 0.9 = -0.640312424 x + 0.9 = -0.640312424 Reorder the terms: 0.9 + x = -0.640312424 Solving 0.9 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.640312424 + -0.9 x = -0.640312424 + -0.9 Combine like terms: -0.640312424 + -0.9 = -1.540312424 x = -1.540312424 Simplifying x = -1.540312424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.259687576, -1.540312424}

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