3x^2-29x-7=0

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Solution for 3x^2-29x-7=0 equation: 


Simplifying
3x2 + -29x + -7 = 0

Reorder the terms:
-7 + -29x + 3x2 = 0

Solving
-7 + -29x + 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'.
-2.333333333 + -9.666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -9.666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -9.666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -9.666666667x + x2 = 0 + 2.333333333
-9.666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-9.666666667x + x2 = 2.333333333

The x term is -9.666666667x.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667x + 23.36111112 + x2 = 2.333333333 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667x + x2 = 2.333333333 + 23.36111112

Combine like terms: 2.333333333 + 23.36111112 = 25.694444453
23.36111112 + -9.666666667x + x2 = 25.694444453

Factor a perfect square on the left side:
(x + -4.833333334)(x + -4.833333334) = 25.694444453

Calculate the square root of the right side: 5.068968776

Break this problem into two subproblems by setting 
(x + -4.833333334) equal to 5.068968776 and -5.068968776.


Subproblem 1
x + -4.833333334 = 5.068968776

Simplifying
x + -4.833333334 = 5.068968776

Reorder the terms:
-4.833333334 + x = 5.068968776

Solving
-4.833333334 + x = 5.068968776

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = 5.068968776 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = 5.068968776 + 4.833333334
x = 5.068968776 + 4.833333334

Combine like terms: 5.068968776 + 4.833333334 = 9.90230211
x = 9.90230211

Simplifying
x = 9.90230211


Subproblem 2
x + -4.833333334 = -5.068968776

Simplifying
x + -4.833333334 = -5.068968776

Reorder the terms:
-4.833333334 + x = -5.068968776

Solving
-4.833333334 + x = -5.068968776

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = -5.068968776 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = -5.068968776 + 4.833333334
x = -5.068968776 + 4.833333334

Combine like terms: -5.068968776 + 4.833333334 = -0.235635442
x = -0.235635442

Simplifying
x = -0.235635442


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.90230211, -0.235635442}

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