(x+6)5x+7=0

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Solution for (x+6)5x+7=0 equation:


Simplifying
(x + 6) * 5x + 7 = 0

Reorder the terms:
(6 + x) * 5x + 7 = 0

Reorder the terms for easier multiplication:
5x(6 + x) + 7 = 0
(6 * 5x + x * 5x) + 7 = 0
(30x + 5x2) + 7 = 0

Reorder the terms:
7 + 30x + 5x2 = 0

Solving
7 + 30x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
1.4 + 6x + x2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 6x + -1.4 + x2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 6x + x2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 6x + x2 = 0 + -1.4
6x + x2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
6x + x2 = -1.4

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -1.4 + 9

Reorder the terms:
9 + 6x + x2 = -1.4 + 9

Combine like terms: -1.4 + 9 = 7.6
9 + 6x + x2 = 7.6

Factor a perfect square on the left side:
(x + 3)(x + 3) = 7.6

Calculate the square root of the right side: 2.75680975

Break this problem into two subproblems by setting 
(x + 3) equal to 2.75680975 and -2.75680975.

Subproblem 1

x + 3 = 2.75680975 Simplifying x + 3 = 2.75680975 Reorder the terms: 3 + x = 2.75680975 Solving 3 + x = 2.75680975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.75680975 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.75680975 + -3 x = 2.75680975 + -3 Combine like terms: 2.75680975 + -3 = -0.24319025 x = -0.24319025 Simplifying x = -0.24319025

Subproblem 2

x + 3 = -2.75680975 Simplifying x + 3 = -2.75680975 Reorder the terms: 3 + x = -2.75680975 Solving 3 + x = -2.75680975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.75680975 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.75680975 + -3 x = -2.75680975 + -3 Combine like terms: -2.75680975 + -3 = -5.75680975 x = -5.75680975 Simplifying x = -5.75680975

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.24319025, -5.75680975}

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