5x^2y+75xy-35y=

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Solution for 5x^2y+75xy-35y= equation:


Simplifying
5x2y + 75xy + -35y = 0

Reorder the terms:
75xy + 5x2y + -35y = 0

Solving
75xy + 5x2y + -35y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(15x + x2 + -7) = 0

Ignore the factor 5.

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 + -7)' equal to zero and attempt to solve: Simplifying 15x + x2 + -7 = 0 Reorder the terms: -7 + 15x + x2 = 0 Solving -7 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 15x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 15x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 15x + x2 = 0 + 7 15x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 15x + x2 = 7 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 = 7 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 7 + 56.25 Combine like terms: 7 + 56.25 = 63.25 56.25 + 15x + x2 = 63.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + 7.5) equal to 7.95298686 and -7.95298686.

Subproblem 1

x + 7.5 = 7.95298686 Simplifying x + 7.5 = 7.95298686 Reorder the terms: 7.5 + x = 7.95298686 Solving 7.5 + x = 7.95298686 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 = 7.95298686 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.95298686 + -7.5 x = 7.95298686 + -7.5 Combine like terms: 7.95298686 + -7.5 = 0.45298686 x = 0.45298686 Simplifying x = 0.45298686

Subproblem 2

x + 7.5 = -7.95298686 Simplifying x + 7.5 = -7.95298686 Reorder the terms: 7.5 + x = -7.95298686 Solving 7.5 + x = -7.95298686 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 = -7.95298686 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.95298686 + -7.5 x = -7.95298686 + -7.5 Combine like terms: -7.95298686 + -7.5 = -15.45298686 x = -15.45298686 Simplifying x = -15.45298686

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.45298686, -15.45298686}

Solution

x = {0.45298686, -15.45298686}

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