60x^2+20x=185

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Solution for 60x^2+20x=185 equation:


Simplifying
60x2 + 20x = 185

Reorder the terms:
20x + 60x2 = 185

Solving
20x + 60x2 = 185

Solving for variable 'x'.

Reorder the terms:
-185 + 20x + 60x2 = 185 + -185

Combine like terms: 185 + -185 = 0
-185 + 20x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-37 + 4x + 12x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-37 + 4x + 12x2)' equal to zero and attempt to solve: Simplifying -37 + 4x + 12x2 = 0 Solving -37 + 4x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.083333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '3.083333333' to each side of the equation. -3.083333333 + 0.3333333333x + 3.083333333 + x2 = 0 + 3.083333333 Reorder the terms: -3.083333333 + 3.083333333 + 0.3333333333x + x2 = 0 + 3.083333333 Combine like terms: -3.083333333 + 3.083333333 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + 3.083333333 0.3333333333x + x2 = 0 + 3.083333333 Combine like terms: 0 + 3.083333333 = 3.083333333 0.3333333333x + x2 = 3.083333333 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 3.083333333 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 3.083333333 + 0.02777777779 Combine like terms: 3.083333333 + 0.02777777779 = 3.11111111079 0.02777777779 + 0.3333333333x + x2 = 3.11111111079 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 3.11111111079 Calculate the square root of the right side: 1.763834207 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.763834207 and -1.763834207.

Subproblem 1

x + 0.1666666667 = 1.763834207 Simplifying x + 0.1666666667 = 1.763834207 Reorder the terms: 0.1666666667 + x = 1.763834207 Solving 0.1666666667 + x = 1.763834207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 1.763834207 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.763834207 + -0.1666666667 x = 1.763834207 + -0.1666666667 Combine like terms: 1.763834207 + -0.1666666667 = 1.5971675403 x = 1.5971675403 Simplifying x = 1.5971675403

Subproblem 2

x + 0.1666666667 = -1.763834207 Simplifying x + 0.1666666667 = -1.763834207 Reorder the terms: 0.1666666667 + x = -1.763834207 Solving 0.1666666667 + x = -1.763834207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -1.763834207 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.763834207 + -0.1666666667 x = -1.763834207 + -0.1666666667 Combine like terms: -1.763834207 + -0.1666666667 = -1.9305008737 x = -1.9305008737 Simplifying x = -1.9305008737

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5971675403, -1.9305008737}

Solution

x = {1.5971675403, -1.9305008737}

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