3x^2+4x-420=0

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Solution for 3x^2+4x-420=0 equation:


Simplifying
3x2 + 4x + -420 = 0

Reorder the terms:
-420 + 4x + 3x2 = 0

Solving
-420 + 4x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-140 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + 1.333333333x + 140 + x2 = 0 + 140

Reorder the terms:
-140 + 140 + 1.333333333x + x2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 1.333333333x + x2 = 0 + 140
1.333333333x + x2 = 0 + 140

Combine like terms: 0 + 140 = 140
1.333333333x + x2 = 140

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 140 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 140 + 0.4444444442

Combine like terms: 140 + 0.4444444442 = 140.4444444442
0.4444444442 + 1.333333333x + x2 = 140.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 140.4444444442

Calculate the square root of the right side: 11.85092589

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 11.85092589 and -11.85092589.

Subproblem 1

x + 0.6666666665 = 11.85092589 Simplifying x + 0.6666666665 = 11.85092589 Reorder the terms: 0.6666666665 + x = 11.85092589 Solving 0.6666666665 + x = 11.85092589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 11.85092589 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 11.85092589 + -0.6666666665 x = 11.85092589 + -0.6666666665 Combine like terms: 11.85092589 + -0.6666666665 = 11.1842592235 x = 11.1842592235 Simplifying x = 11.1842592235

Subproblem 2

x + 0.6666666665 = -11.85092589 Simplifying x + 0.6666666665 = -11.85092589 Reorder the terms: 0.6666666665 + x = -11.85092589 Solving 0.6666666665 + x = -11.85092589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -11.85092589 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -11.85092589 + -0.6666666665 x = -11.85092589 + -0.6666666665 Combine like terms: -11.85092589 + -0.6666666665 = -12.5175925565 x = -12.5175925565 Simplifying x = -12.5175925565

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.1842592235, -12.5175925565}

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