7x^2+58x+6=0

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Solution for 7x^2+58x+6=0 equation:


Simplifying
7x2 + 58x + 6 = 0

Reorder the terms:
6 + 58x + 7x2 = 0

Solving
6 + 58x + 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'.
0.8571428571 + 8.285714286x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + 8.285714286x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + 8.285714286x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + 8.285714286x + x2 = 0 + -0.8571428571
8.285714286x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
8.285714286x + x2 = -0.8571428571

The x term is 8.285714286x.  Take half its coefficient (4.142857143).
Square it (17.16326531) and add it to both sides.

Add '17.16326531' to each side of the equation.
8.285714286x + 17.16326531 + x2 = -0.8571428571 + 17.16326531

Reorder the terms:
17.16326531 + 8.285714286x + x2 = -0.8571428571 + 17.16326531

Combine like terms: -0.8571428571 + 17.16326531 = 16.3061224529
17.16326531 + 8.285714286x + x2 = 16.3061224529

Factor a perfect square on the left side:
(x + 4.142857143)(x + 4.142857143) = 16.3061224529

Calculate the square root of the right side: 4.038084008

Break this problem into two subproblems by setting 
(x + 4.142857143) equal to 4.038084008 and -4.038084008.

Subproblem 1

x + 4.142857143 = 4.038084008 Simplifying x + 4.142857143 = 4.038084008 Reorder the terms: 4.142857143 + x = 4.038084008 Solving 4.142857143 + x = 4.038084008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.142857143' to each side of the equation. 4.142857143 + -4.142857143 + x = 4.038084008 + -4.142857143 Combine like terms: 4.142857143 + -4.142857143 = 0.000000000 0.000000000 + x = 4.038084008 + -4.142857143 x = 4.038084008 + -4.142857143 Combine like terms: 4.038084008 + -4.142857143 = -0.104773135 x = -0.104773135 Simplifying x = -0.104773135

Subproblem 2

x + 4.142857143 = -4.038084008 Simplifying x + 4.142857143 = -4.038084008 Reorder the terms: 4.142857143 + x = -4.038084008 Solving 4.142857143 + x = -4.038084008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.142857143' to each side of the equation. 4.142857143 + -4.142857143 + x = -4.038084008 + -4.142857143 Combine like terms: 4.142857143 + -4.142857143 = 0.000000000 0.000000000 + x = -4.038084008 + -4.142857143 x = -4.038084008 + -4.142857143 Combine like terms: -4.038084008 + -4.142857143 = -8.180941151 x = -8.180941151 Simplifying x = -8.180941151

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.104773135, -8.180941151}

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