5(3c-5)7c=-41

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Solution for 5(3c-5)7c=-41 equation:


Simplifying
5(3c + -5) * 7c = -41

Reorder the terms:
5(-5 + 3c) * 7c = -41

Reorder the terms for easier multiplication:
5 * 7c(-5 + 3c) = -41

Multiply 5 * 7
35c(-5 + 3c) = -41
(-5 * 35c + 3c * 35c) = -41
(-175c + 105c2) = -41

Solving
-175c + 105c2 = -41

Solving for variable 'c'.

Reorder the terms:
41 + -175c + 105c2 = -41 + 41

Combine like terms: -41 + 41 = 0
41 + -175c + 105c2 = 0

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

Divide each side by '105'.
0.3904761905 + -1.666666667c + c2 = 0

Move the constant term to the right:

Add '-0.3904761905' to each side of the equation.
0.3904761905 + -1.666666667c + -0.3904761905 + c2 = 0 + -0.3904761905

Reorder the terms:
0.3904761905 + -0.3904761905 + -1.666666667c + c2 = 0 + -0.3904761905

Combine like terms: 0.3904761905 + -0.3904761905 = 0.0000000000
0.0000000000 + -1.666666667c + c2 = 0 + -0.3904761905
-1.666666667c + c2 = 0 + -0.3904761905

Combine like terms: 0 + -0.3904761905 = -0.3904761905
-1.666666667c + c2 = -0.3904761905

The c term is -1.666666667c.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667c + 0.6944444447 + c2 = -0.3904761905 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667c + c2 = -0.3904761905 + 0.6944444447

Combine like terms: -0.3904761905 + 0.6944444447 = 0.3039682542
0.6944444447 + -1.666666667c + c2 = 0.3039682542

Factor a perfect square on the left side:
(c + -0.8333333335)(c + -0.8333333335) = 0.3039682542

Calculate the square root of the right side: 0.551333161

Break this problem into two subproblems by setting 
(c + -0.8333333335) equal to 0.551333161 and -0.551333161.

Subproblem 1

c + -0.8333333335 = 0.551333161 Simplifying c + -0.8333333335 = 0.551333161 Reorder the terms: -0.8333333335 + c = 0.551333161 Solving -0.8333333335 + c = 0.551333161 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + c = 0.551333161 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + c = 0.551333161 + 0.8333333335 c = 0.551333161 + 0.8333333335 Combine like terms: 0.551333161 + 0.8333333335 = 1.3846664945 c = 1.3846664945 Simplifying c = 1.3846664945

Subproblem 2

c + -0.8333333335 = -0.551333161 Simplifying c + -0.8333333335 = -0.551333161 Reorder the terms: -0.8333333335 + c = -0.551333161 Solving -0.8333333335 + c = -0.551333161 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + c = -0.551333161 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + c = -0.551333161 + 0.8333333335 c = -0.551333161 + 0.8333333335 Combine like terms: -0.551333161 + 0.8333333335 = 0.2820001725 c = 0.2820001725 Simplifying c = 0.2820001725

Solution

The solution to the problem is based on the solutions from the subproblems. c = {1.3846664945, 0.2820001725}

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