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Simplifying 7x2y + 91xy + -49y = 0 Reorder the terms: 91xy + 7x2y + -49y = 0 Solving 91xy + 7x2y + -49y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7y'. 7y(13x + x2 + -7) = 0 Ignore the factor 7.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 '(13x + x2 + -7)' equal to zero and attempt to solve: Simplifying 13x + x2 + -7 = 0 Reorder the terms: -7 + 13x + x2 = 0 Solving -7 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 13x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 13x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 13x + x2 = 0 + 7 13x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 13x + x2 = 7 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 7 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 7 + 42.25 Combine like terms: 7 + 42.25 = 49.25 42.25 + 13x + x2 = 49.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (x + 6.5) equal to 7.017834424 and -7.017834424.Subproblem 1
x + 6.5 = 7.017834424 Simplifying x + 6.5 = 7.017834424 Reorder the terms: 6.5 + x = 7.017834424 Solving 6.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.017834424 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.017834424 + -6.5 x = 7.017834424 + -6.5 Combine like terms: 7.017834424 + -6.5 = 0.517834424 x = 0.517834424 Simplifying x = 0.517834424Subproblem 2
x + 6.5 = -7.017834424 Simplifying x + 6.5 = -7.017834424 Reorder the terms: 6.5 + x = -7.017834424 Solving 6.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.017834424 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.017834424 + -6.5 x = -7.017834424 + -6.5 Combine like terms: -7.017834424 + -6.5 = -13.517834424 x = -13.517834424 Simplifying x = -13.517834424Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.517834424, -13.517834424}Solution
x = {0.517834424, -13.517834424}
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