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Simplifying (7p + 1) * x2 + (5p + -1) * x + 1 = 1 Reorder the terms: (1 + 7p) * x2 + (5p + -1) * x + 1 = 1 Reorder the terms for easier multiplication: x2(1 + 7p) + (5p + -1) * x + 1 = 1 (1 * x2 + 7p * x2) + (5p + -1) * x + 1 = 1 Reorder the terms: (7px2 + 1x2) + (5p + -1) * x + 1 = 1 (7px2 + 1x2) + (5p + -1) * x + 1 = 1 Reorder the terms: 7px2 + 1x2 + (-1 + 5p) * x + 1 = 1 Reorder the terms for easier multiplication: 7px2 + 1x2 + x(-1 + 5p) + 1 = 1 7px2 + 1x2 + (-1 * x + 5p * x) + 1 = 1 Reorder the terms: 7px2 + 1x2 + (5px + -1x) + 1 = 1 7px2 + 1x2 + (5px + -1x) + 1 = 1 Reorder the terms: 1 + 5px + 7px2 + -1x + 1x2 = 1 Add '-1' to each side of the equation. 1 + 5px + 7px2 + -1x + -1 + 1x2 = 1 + -1 Reorder the terms: 1 + -1 + 5px + 7px2 + -1x + 1x2 = 1 + -1 Combine like terms: 1 + -1 = 0 0 + 5px + 7px2 + -1x + 1x2 = 1 + -1 5px + 7px2 + -1x + 1x2 = 1 + -1 Combine like terms: 1 + -1 = 0 5px + 7px2 + -1x + 1x2 = 0 Solving 5px + 7px2 + -1x + 1x2 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add 'x' to each side of the equation. 5px + 7px2 + -1x + x + 1x2 = 0 + x Combine like terms: -1x + x = 0 5px + 7px2 + 0 + 1x2 = 0 + x 5px + 7px2 + 1x2 = 0 + x Remove the zero: 5px + 7px2 + 1x2 = x Add '-1x2' to each side of the equation. 5px + 7px2 + 1x2 + -1x2 = x + -1x2 Combine like terms: 1x2 + -1x2 = 0 5px + 7px2 + 0 = x + -1x2 5px + 7px2 = x + -1x2 Reorder the terms: 5px + 7px2 + -1x + x2 = x + -1x + -1x2 + x2 Combine like terms: x + -1x = 0 5px + 7px2 + -1x + x2 = 0 + -1x2 + x2 5px + 7px2 + -1x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 5px + 7px2 + -1x + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(5p + 7px + -1 + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing p to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(5p + 7px + -1 + x)' equal to zero and attempt to solve: Simplifying 5p + 7px + -1 + x = 0 Reorder the terms: -1 + 5p + 7px + x = 0 Solving -1 + 5p + 7px + x = 0 Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 5p + 7px + 1 + x = 0 + 1 Reorder the terms: -1 + 1 + 5p + 7px + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5p + 7px + x = 0 + 1 5p + 7px + x = 0 + 1 Combine like terms: 0 + 1 = 1 5p + 7px + x = 1 Add '-1x' to each side of the equation. 5p + 7px + x + -1x = 1 + -1x Combine like terms: x + -1x = 0 5p + 7px + 0 = 1 + -1x 5p + 7px = 1 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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