4x^2y+60xy-52y=

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Solution for 4x^2y+60xy-52y= equation:


Simplifying
4x2y + 60xy + -52y = 0

Reorder the terms:
60xy + 4x2y + -52y = 0

Solving
60xy + 4x2y + -52y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(15x + x2 + -13) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(15x + x2 + -13)' equal to zero and attempt to solve: Simplifying 15x + x2 + -13 = 0 Reorder the terms: -13 + 15x + x2 = 0 Solving -13 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 15x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 15x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 15x + x2 = 0 + 13 15x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 15x + x2 = 13 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 13 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 13 + 56.25 Combine like terms: 13 + 56.25 = 69.25 56.25 + 15x + x2 = 69.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + 7.5) equal to 8.321658489 and -8.321658489.

Subproblem 1

x + 7.5 = 8.321658489 Simplifying x + 7.5 = 8.321658489 Reorder the terms: 7.5 + x = 8.321658489 Solving 7.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.321658489 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.321658489 + -7.5 x = 8.321658489 + -7.5 Combine like terms: 8.321658489 + -7.5 = 0.821658489 x = 0.821658489 Simplifying x = 0.821658489

Subproblem 2

x + 7.5 = -8.321658489 Simplifying x + 7.5 = -8.321658489 Reorder the terms: 7.5 + x = -8.321658489 Solving 7.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.321658489 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.321658489 + -7.5 x = -8.321658489 + -7.5 Combine like terms: -8.321658489 + -7.5 = -15.821658489 x = -15.821658489 Simplifying x = -15.821658489

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.821658489, -15.821658489}

Solution

x = {0.821658489, -15.821658489}

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