3x^2+4x-51=0

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Solution for 3x^2+4x-51=0 equation:


Simplifying
3x2 + 4x + -51 = 0

Reorder the terms:
-51 + 4x + 3x2 = 0

Solving
-51 + 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'.
-17 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 1.333333333x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 1.333333333x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 1.333333333x + x2 = 0 + 17
1.333333333x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
1.333333333x + x2 = 17

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 = 17 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 17 + 0.4444444442

Combine like terms: 17 + 0.4444444442 = 17.4444444442
0.4444444442 + 1.333333333x + x2 = 17.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 17.4444444442

Calculate the square root of the right side: 4.176654695

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 4.176654695 and -4.176654695.

Subproblem 1

x + 0.6666666665 = 4.176654695 Simplifying x + 0.6666666665 = 4.176654695 Reorder the terms: 0.6666666665 + x = 4.176654695 Solving 0.6666666665 + x = 4.176654695 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 = 4.176654695 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 4.176654695 + -0.6666666665 x = 4.176654695 + -0.6666666665 Combine like terms: 4.176654695 + -0.6666666665 = 3.5099880285 x = 3.5099880285 Simplifying x = 3.5099880285

Subproblem 2

x + 0.6666666665 = -4.176654695 Simplifying x + 0.6666666665 = -4.176654695 Reorder the terms: 0.6666666665 + x = -4.176654695 Solving 0.6666666665 + x = -4.176654695 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 = -4.176654695 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -4.176654695 + -0.6666666665 x = -4.176654695 + -0.6666666665 Combine like terms: -4.176654695 + -0.6666666665 = -4.8433213615 x = -4.8433213615 Simplifying x = -4.8433213615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.5099880285, -4.8433213615}

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