2x^2+9x+2=

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Solution for 2x^2+9x+2= equation:


Simplifying
2x2 + 9x + 2 = 0

Reorder the terms:
2 + 9x + 2x2 = 0

Solving
2 + 9x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
1 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 4.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4.5x + x2 = 0 + -1
4.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4.5x + x2 = -1

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -1 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -1 + 5.0625

Combine like terms: -1 + 5.0625 = 4.0625
5.0625 + 4.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.015564437 and -2.015564437.

Subproblem 1

x + 2.25 = 2.015564437 Simplifying x + 2.25 = 2.015564437 Reorder the terms: 2.25 + x = 2.015564437 Solving 2.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.015564437 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.015564437 + -2.25 x = 2.015564437 + -2.25 Combine like terms: 2.015564437 + -2.25 = -0.234435563 x = -0.234435563 Simplifying x = -0.234435563

Subproblem 2

x + 2.25 = -2.015564437 Simplifying x + 2.25 = -2.015564437 Reorder the terms: 2.25 + x = -2.015564437 Solving 2.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.015564437 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.015564437 + -2.25 x = -2.015564437 + -2.25 Combine like terms: -2.015564437 + -2.25 = -4.265564437 x = -4.265564437 Simplifying x = -4.265564437

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.234435563, -4.265564437}

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