7x^2-34x-15=0

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Solution for 7x^2-34x-15=0 equation: 


Simplifying
7x2 + -34x + -15 = 0

Reorder the terms:
-15 + -34x + 7x2 = 0

Solving
-15 + -34x + 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'.
-2.142857143 + -4.857142857x + x2 = 0

Move the constant term to the right:

Add '2.142857143' to each side of the equation.
-2.142857143 + -4.857142857x + 2.142857143 + x2 = 0 + 2.142857143

Reorder the terms:
-2.142857143 + 2.142857143 + -4.857142857x + x2 = 0 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + -4.857142857x + x2 = 0 + 2.142857143
-4.857142857x + x2 = 0 + 2.142857143

Combine like terms: 0 + 2.142857143 = 2.142857143
-4.857142857x + x2 = 2.142857143

The x term is -4.857142857x.  Take half its coefficient (-2.428571429).
Square it (5.897959186) and add it to both sides.

Add '5.897959186' to each side of the equation.
-4.857142857x + 5.897959186 + x2 = 2.142857143 + 5.897959186

Reorder the terms:
5.897959186 + -4.857142857x + x2 = 2.142857143 + 5.897959186

Combine like terms: 2.142857143 + 5.897959186 = 8.040816329
5.897959186 + -4.857142857x + x2 = 8.040816329

Factor a perfect square on the left side:
(x + -2.428571429)(x + -2.428571429) = 8.040816329

Calculate the square root of the right side: 2.835633321

Break this problem into two subproblems by setting 
(x + -2.428571429) equal to 2.835633321 and -2.835633321.


Subproblem 1
x + -2.428571429 = 2.835633321

Simplifying
x + -2.428571429 = 2.835633321

Reorder the terms:
-2.428571429 + x = 2.835633321

Solving
-2.428571429 + x = 2.835633321

Solving for variable 'x'.

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

Add '2.428571429' to each side of the equation.
-2.428571429 + 2.428571429 + x = 2.835633321 + 2.428571429

Combine like terms: -2.428571429 + 2.428571429 = 0.000000000
0.000000000 + x = 2.835633321 + 2.428571429
x = 2.835633321 + 2.428571429

Combine like terms: 2.835633321 + 2.428571429 = 5.26420475
x = 5.26420475

Simplifying
x = 5.26420475


Subproblem 2
x + -2.428571429 = -2.835633321

Simplifying
x + -2.428571429 = -2.835633321

Reorder the terms:
-2.428571429 + x = -2.835633321

Solving
-2.428571429 + x = -2.835633321

Solving for variable 'x'.

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

Add '2.428571429' to each side of the equation.
-2.428571429 + 2.428571429 + x = -2.835633321 + 2.428571429

Combine like terms: -2.428571429 + 2.428571429 = 0.000000000
0.000000000 + x = -2.835633321 + 2.428571429
x = -2.835633321 + 2.428571429

Combine like terms: -2.835633321 + 2.428571429 = -0.407061892
x = -0.407061892

Simplifying
x = -0.407061892


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.26420475, -0.407061892}

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