(5-x)*(6x+2)=5

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


Simplifying
(5 + -1x)(6x + 2) = 5

Reorder the terms:
(5 + -1x)(2 + 6x) = 5

Multiply (5 + -1x) * (2 + 6x)
(5(2 + 6x) + -1x * (2 + 6x)) = 5
((2 * 5 + 6x * 5) + -1x * (2 + 6x)) = 5
((10 + 30x) + -1x * (2 + 6x)) = 5
(10 + 30x + (2 * -1x + 6x * -1x)) = 5
(10 + 30x + (-2x + -6x2)) = 5

Combine like terms: 30x + -2x = 28x
(10 + 28x + -6x2) = 5

Solving
10 + 28x + -6x2 = 5

Solving for variable 'x'.

Reorder the terms:
10 + -5 + 28x + -6x2 = 5 + -5

Combine like terms: 10 + -5 = 5
5 + 28x + -6x2 = 5 + -5

Combine like terms: 5 + -5 = 0
5 + 28x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.8333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -4.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -4.666666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -4.666666667x + x2 = 0 + 0.8333333333
-4.666666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-4.666666667x + x2 = 0.8333333333

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 0.8333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 0.8333333333 + 5.444444448

Combine like terms: 0.8333333333 + 5.444444448 = 6.2777777813
5.444444448 + -4.666666667x + x2 = 6.2777777813

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 6.2777777813

Calculate the square root of the right side: 2.505549397

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.505549397 and -2.505549397.

Subproblem 1

x + -2.333333334 = 2.505549397 Simplifying x + -2.333333334 = 2.505549397 Reorder the terms: -2.333333334 + x = 2.505549397 Solving -2.333333334 + x = 2.505549397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.505549397 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.505549397 + 2.333333334 x = 2.505549397 + 2.333333334 Combine like terms: 2.505549397 + 2.333333334 = 4.838882731 x = 4.838882731 Simplifying x = 4.838882731

Subproblem 2

x + -2.333333334 = -2.505549397 Simplifying x + -2.333333334 = -2.505549397 Reorder the terms: -2.333333334 + x = -2.505549397 Solving -2.333333334 + x = -2.505549397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.505549397 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.505549397 + 2.333333334 x = -2.505549397 + 2.333333334 Combine like terms: -2.505549397 + 2.333333334 = -0.172216063 x = -0.172216063 Simplifying x = -0.172216063

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.838882731, -0.172216063}

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