(6x)(6x)+7x-5=0

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


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

Remove parenthesis around (6x)
6x(6x) + 7x + -5 = 0

Remove parenthesis around (6x)
6x * 6x + 7x + -5 = 0

Reorder the terms for easier multiplication:
6 * 6x * x + 7x + -5 = 0

Multiply 6 * 6
36x * x + 7x + -5 = 0

Multiply x * x
36x2 + 7x + -5 = 0

Reorder the terms:
-5 + 7x + 36x2 = 0

Solving
-5 + 7x + 36x2 = 0

Solving for variable 'x'.

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

Divide each side by '36'.
-0.1388888889 + 0.1944444444x + x2 = 0

Move the constant term to the right:

Add '0.1388888889' to each side of the equation.
-0.1388888889 + 0.1944444444x + 0.1388888889 + x2 = 0 + 0.1388888889

Reorder the terms:
-0.1388888889 + 0.1388888889 + 0.1944444444x + x2 = 0 + 0.1388888889

Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000
0.0000000000 + 0.1944444444x + x2 = 0 + 0.1388888889
0.1944444444x + x2 = 0 + 0.1388888889

Combine like terms: 0 + 0.1388888889 = 0.1388888889
0.1944444444x + x2 = 0.1388888889

The x term is 0.1944444444x.  Take half its coefficient (0.0972222222).
Square it (0.009452160490) and add it to both sides.

Add '0.009452160490' to each side of the equation.
0.1944444444x + 0.009452160490 + x2 = 0.1388888889 + 0.009452160490

Reorder the terms:
0.009452160490 + 0.1944444444x + x2 = 0.1388888889 + 0.009452160490

Combine like terms: 0.1388888889 + 0.009452160490 = 0.14834104939
0.009452160490 + 0.1944444444x + x2 = 0.14834104939

Factor a perfect square on the left side:
(x + 0.0972222222)(x + 0.0972222222) = 0.14834104939

Calculate the square root of the right side: 0.385150684

Break this problem into two subproblems by setting 
(x + 0.0972222222) equal to 0.385150684 and -0.385150684.

Subproblem 1

x + 0.0972222222 = 0.385150684 Simplifying x + 0.0972222222 = 0.385150684 Reorder the terms: 0.0972222222 + x = 0.385150684 Solving 0.0972222222 + x = 0.385150684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0972222222' to each side of the equation. 0.0972222222 + -0.0972222222 + x = 0.385150684 + -0.0972222222 Combine like terms: 0.0972222222 + -0.0972222222 = 0.0000000000 0.0000000000 + x = 0.385150684 + -0.0972222222 x = 0.385150684 + -0.0972222222 Combine like terms: 0.385150684 + -0.0972222222 = 0.2879284618 x = 0.2879284618 Simplifying x = 0.2879284618

Subproblem 2

x + 0.0972222222 = -0.385150684 Simplifying x + 0.0972222222 = -0.385150684 Reorder the terms: 0.0972222222 + x = -0.385150684 Solving 0.0972222222 + x = -0.385150684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0972222222' to each side of the equation. 0.0972222222 + -0.0972222222 + x = -0.385150684 + -0.0972222222 Combine like terms: 0.0972222222 + -0.0972222222 = 0.0000000000 0.0000000000 + x = -0.385150684 + -0.0972222222 x = -0.385150684 + -0.0972222222 Combine like terms: -0.385150684 + -0.0972222222 = -0.4823729062 x = -0.4823729062 Simplifying x = -0.4823729062

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2879284618, -0.4823729062}

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