9x^2+18x=-4

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Solution for 9x^2+18x=-4 equation:


Simplifying
9x2 + 18x = -4

Reorder the terms:
18x + 9x2 = -4

Solving
18x + 9x2 = -4

Solving for variable 'x'.

Reorder the terms:
4 + 18x + 9x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 18x + 9x2 = 0

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

Divide each side by '9'.
0.4444444444 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + 2x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + 2x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + -0.4444444444
2x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
2x + x2 = -0.4444444444

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.4444444444 + 1

Reorder the terms:
1 + 2x + x2 = -0.4444444444 + 1

Combine like terms: -0.4444444444 + 1 = 0.5555555556
1 + 2x + x2 = 0.5555555556

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.5555555556

Calculate the square root of the right side: 0.745355993

Break this problem into two subproblems by setting 
(x + 1) equal to 0.745355993 and -0.745355993.

Subproblem 1

x + 1 = 0.745355993 Simplifying x + 1 = 0.745355993 Reorder the terms: 1 + x = 0.745355993 Solving 1 + x = 0.745355993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.745355993 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.745355993 + -1 x = 0.745355993 + -1 Combine like terms: 0.745355993 + -1 = -0.254644007 x = -0.254644007 Simplifying x = -0.254644007

Subproblem 2

x + 1 = -0.745355993 Simplifying x + 1 = -0.745355993 Reorder the terms: 1 + x = -0.745355993 Solving 1 + x = -0.745355993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.745355993 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.745355993 + -1 x = -0.745355993 + -1 Combine like terms: -0.745355993 + -1 = -1.745355993 x = -1.745355993 Simplifying x = -1.745355993

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.254644007, -1.745355993}

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