3x^2=-9x-4

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Solution for 3x^2=-9x-4 equation:


Simplifying
3x2 = -9x + -4

Reorder the terms:
3x2 = -4 + -9x

Solving
3x2 = -4 + -9x

Solving for variable 'x'.

Reorder the terms:
4 + 9x + 3x2 = -4 + -9x + 4 + 9x

Reorder the terms:
4 + 9x + 3x2 = -4 + 4 + -9x + 9x

Combine like terms: -4 + 4 = 0
4 + 9x + 3x2 = 0 + -9x + 9x
4 + 9x + 3x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
4 + 9x + 3x2 = 0

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

Divide each side by '3'.
1.333333333 + 3x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 3x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 3x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 3x + x2 = 0 + -1.333333333
3x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
3x + x2 = -1.333333333

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -1.333333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -1.333333333 + 2.25

Combine like terms: -1.333333333 + 2.25 = 0.916666667
2.25 + 3x + x2 = 0.916666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 0.916666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(x + 1.5) equal to 0.957427108 and -0.957427108.

Subproblem 1

x + 1.5 = 0.957427108 Simplifying x + 1.5 = 0.957427108 Reorder the terms: 1.5 + x = 0.957427108 Solving 1.5 + x = 0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.957427108 + -1.5 x = 0.957427108 + -1.5 Combine like terms: 0.957427108 + -1.5 = -0.542572892 x = -0.542572892 Simplifying x = -0.542572892

Subproblem 2

x + 1.5 = -0.957427108 Simplifying x + 1.5 = -0.957427108 Reorder the terms: 1.5 + x = -0.957427108 Solving 1.5 + x = -0.957427108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.957427108 + -1.5 x = -0.957427108 + -1.5 Combine like terms: -0.957427108 + -1.5 = -2.457427108 x = -2.457427108 Simplifying x = -2.457427108

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.542572892, -2.457427108}

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