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Simplifying x3 + x2 = 81x Reorder the terms: x2 + x3 = 81x Solving x2 + x3 = 81x Solving for variable 'x'. Reorder the terms: -81x + x2 + x3 = 81x + -81x Combine like terms: 81x + -81x = 0 -81x + x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-81 + x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-81 + x + x2)' equal to zero and attempt to solve: Simplifying -81 + x + x2 = 0 Solving -81 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + x + x2 = 0 + 81 x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 x + x2 = 81 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 81 + 0.25 Reorder the terms: 0.25 + x + x2 = 81 + 0.25 Combine like terms: 81 + 0.25 = 81.25 0.25 + x + x2 = 81.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + 0.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + 0.5 = 9.013878189 Simplifying x + 0.5 = 9.013878189 Reorder the terms: 0.5 + x = 9.013878189 Solving 0.5 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.013878189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.013878189 + -0.5 x = 9.013878189 + -0.5 Combine like terms: 9.013878189 + -0.5 = 8.513878189 x = 8.513878189 Simplifying x = 8.513878189Subproblem 2
x + 0.5 = -9.013878189 Simplifying x + 0.5 = -9.013878189 Reorder the terms: 0.5 + x = -9.013878189 Solving 0.5 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.013878189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.013878189 + -0.5 x = -9.013878189 + -0.5 Combine like terms: -9.013878189 + -0.5 = -9.513878189 x = -9.513878189 Simplifying x = -9.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.513878189, -9.513878189}Solution
x = {0, 8.513878189, -9.513878189}
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