7x(6x+5)=-2

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Solution for 7x(6x+5)=-2 equation:


Simplifying
7x(6x + 5) = -2

Reorder the terms:
7x(5 + 6x) = -2
(5 * 7x + 6x * 7x) = -2
(35x + 42x2) = -2

Solving
35x + 42x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + 35x + 42x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 35x + 42x2 = 0

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

Divide each side by '42'.
0.04761904762 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '-0.04761904762' to each side of the equation.
0.04761904762 + 0.8333333333x + -0.04761904762 + x2 = 0 + -0.04761904762

Reorder the terms:
0.04761904762 + -0.04761904762 + 0.8333333333x + x2 = 0 + -0.04761904762

Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000
0.00000000000 + 0.8333333333x + x2 = 0 + -0.04761904762
0.8333333333x + x2 = 0 + -0.04761904762

Combine like terms: 0 + -0.04761904762 = -0.04761904762
0.8333333333x + x2 = -0.04761904762

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = -0.04761904762 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = -0.04761904762 + 0.1736111111

Combine like terms: -0.04761904762 + 0.1736111111 = 0.12599206348
0.1736111111 + 0.8333333333x + x2 = 0.12599206348

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 0.12599206348

Calculate the square root of the right side: 0.354953608

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 0.354953608 and -0.354953608.

Subproblem 1

x + 0.4166666667 = 0.354953608 Simplifying x + 0.4166666667 = 0.354953608 Reorder the terms: 0.4166666667 + x = 0.354953608 Solving 0.4166666667 + x = 0.354953608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 0.354953608 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 0.354953608 + -0.4166666667 x = 0.354953608 + -0.4166666667 Combine like terms: 0.354953608 + -0.4166666667 = -0.0617130587 x = -0.0617130587 Simplifying x = -0.0617130587

Subproblem 2

x + 0.4166666667 = -0.354953608 Simplifying x + 0.4166666667 = -0.354953608 Reorder the terms: 0.4166666667 + x = -0.354953608 Solving 0.4166666667 + x = -0.354953608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -0.354953608 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -0.354953608 + -0.4166666667 x = -0.354953608 + -0.4166666667 Combine like terms: -0.354953608 + -0.4166666667 = -0.7716202747 x = -0.7716202747 Simplifying x = -0.7716202747

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.0617130587, -0.7716202747}

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