7x^2-29x-46=0

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Solution for 7x^2-29x-46=0 equation: 


Simplifying
7x2 + -29x + -46 = 0

Reorder the terms:
-46 + -29x + 7x2 = 0

Solving
-46 + -29x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-6.571428571 + -4.142857143x + x2 = 0

Move the constant term to the right:

Add '6.571428571' to each side of the equation.
-6.571428571 + -4.142857143x + 6.571428571 + x2 = 0 + 6.571428571

Reorder the terms:
-6.571428571 + 6.571428571 + -4.142857143x + x2 = 0 + 6.571428571

Combine like terms: -6.571428571 + 6.571428571 = 0.000000000
0.000000000 + -4.142857143x + x2 = 0 + 6.571428571
-4.142857143x + x2 = 0 + 6.571428571

Combine like terms: 0 + 6.571428571 = 6.571428571
-4.142857143x + x2 = 6.571428571

The x term is -4.142857143x.  Take half its coefficient (-2.071428572).
Square it (4.290816329) and add it to both sides.

Add '4.290816329' to each side of the equation.
-4.142857143x + 4.290816329 + x2 = 6.571428571 + 4.290816329

Reorder the terms:
4.290816329 + -4.142857143x + x2 = 6.571428571 + 4.290816329

Combine like terms: 6.571428571 + 4.290816329 = 10.8622449
4.290816329 + -4.142857143x + x2 = 10.8622449

Factor a perfect square on the left side:
(x + -2.071428572)(x + -2.071428572) = 10.8622449

Calculate the square root of the right side: 3.295791999

Break this problem into two subproblems by setting 
(x + -2.071428572) equal to 3.295791999 and -3.295791999.


Subproblem 1
x + -2.071428572 = 3.295791999

Simplifying
x + -2.071428572 = 3.295791999

Reorder the terms:
-2.071428572 + x = 3.295791999

Solving
-2.071428572 + x = 3.295791999

Solving for variable 'x'.

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

Add '2.071428572' to each side of the equation.
-2.071428572 + 2.071428572 + x = 3.295791999 + 2.071428572

Combine like terms: -2.071428572 + 2.071428572 = 0.000000000
0.000000000 + x = 3.295791999 + 2.071428572
x = 3.295791999 + 2.071428572

Combine like terms: 3.295791999 + 2.071428572 = 5.367220571
x = 5.367220571

Simplifying
x = 5.367220571


Subproblem 2
x + -2.071428572 = -3.295791999

Simplifying
x + -2.071428572 = -3.295791999

Reorder the terms:
-2.071428572 + x = -3.295791999

Solving
-2.071428572 + x = -3.295791999

Solving for variable 'x'.

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

Add '2.071428572' to each side of the equation.
-2.071428572 + 2.071428572 + x = -3.295791999 + 2.071428572

Combine like terms: -2.071428572 + 2.071428572 = 0.000000000
0.000000000 + x = -3.295791999 + 2.071428572
x = -3.295791999 + 2.071428572

Combine like terms: -3.295791999 + 2.071428572 = -1.224363427
x = -1.224363427

Simplifying
x = -1.224363427


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.367220571, -1.224363427}

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