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Simplifying x3 = (x2 + 1000x) Reorder the terms: x3 = (1000x + x2) Remove parenthesis around (1000x + x2) x3 = 1000x + x2 Solving x3 = 1000x + x2 Solving for variable 'x'. Reorder the terms: -1000x + -1x2 + x3 = 1000x + x2 + -1000x + -1x2 Reorder the terms: -1000x + -1x2 + x3 = 1000x + -1000x + x2 + -1x2 Combine like terms: 1000x + -1000x = 0 -1000x + -1x2 + x3 = 0 + x2 + -1x2 -1000x + -1x2 + x3 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1000x + -1x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1000 + -1x + 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 '(-1000 + -1x + x2)' equal to zero and attempt to solve: Simplifying -1000 + -1x + x2 = 0 Solving -1000 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -1x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -1x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -1x + x2 = 0 + 1000 -1x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -1x + x2 = 1000 The x term is -1x. 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. -1x + 0.25 + x2 = 1000 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1000 + 0.25 Combine like terms: 1000 + 0.25 = 1000.25 0.25 + -1x + x2 = 1000.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1000.25 Calculate the square root of the right side: 31.626729202 Break this problem into two subproblems by setting (x + -0.5) equal to 31.626729202 and -31.626729202.Subproblem 1
x + -0.5 = 31.626729202 Simplifying x + -0.5 = 31.626729202 Reorder the terms: -0.5 + x = 31.626729202 Solving -0.5 + x = 31.626729202 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 = 31.626729202 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 31.626729202 + 0.5 x = 31.626729202 + 0.5 Combine like terms: 31.626729202 + 0.5 = 32.126729202 x = 32.126729202 Simplifying x = 32.126729202Subproblem 2
x + -0.5 = -31.626729202 Simplifying x + -0.5 = -31.626729202 Reorder the terms: -0.5 + x = -31.626729202 Solving -0.5 + x = -31.626729202 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 = -31.626729202 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -31.626729202 + 0.5 x = -31.626729202 + 0.5 Combine like terms: -31.626729202 + 0.5 = -31.126729202 x = -31.126729202 Simplifying x = -31.126729202Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.126729202, -31.126729202}Solution
x = {0, 32.126729202, -31.126729202}
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