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Simplifying 0 = 5x3 + -1x2 + -10x Reorder the terms: 0 = -10x + -1x2 + 5x3 Solving 0 = -10x + -1x2 + 5x3 Solving for variable 'x'. Remove the zero: 10x + x2 + -5x3 = -10x + -1x2 + 5x3 + 10x + x2 + -5x3 Reorder the terms: 10x + x2 + -5x3 = -10x + 10x + -1x2 + x2 + 5x3 + -5x3 Combine like terms: -10x + 10x = 0 10x + x2 + -5x3 = 0 + -1x2 + x2 + 5x3 + -5x3 10x + x2 + -5x3 = -1x2 + x2 + 5x3 + -5x3 Combine like terms: -1x2 + x2 = 0 10x + x2 + -5x3 = 0 + 5x3 + -5x3 10x + x2 + -5x3 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 10x + x2 + -5x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(10 + x + -5x2) = 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 '(10 + x + -5x2)' equal to zero and attempt to solve: Simplifying 10 + x + -5x2 = 0 Solving 10 + x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2 + -0.2x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.2x + x2 = 0 + 2 -0.2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.2x + x2 = 2 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. -0.2x + 0.25 + x2 = 2 + 0.25 Reorder the terms: 0.25 + -0.2x + x2 = 2 + 0.25 Combine like terms: 2 + 0.25 = 2.25 0.25 + -0.2x + x2 = 2.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + 0.5) equal to 1.5 and -1.5.Subproblem 1
x + 0.5 = 1.5 Simplifying x + 0.5 = 1.5 Reorder the terms: 0.5 + x = 1.5 Solving 0.5 + x = 1.5 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 = 1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.5 + -0.5 x = 1.5 + -0.5 Combine like terms: 1.5 + -0.5 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 0.5 = -1.5 Simplifying x + 0.5 = -1.5 Reorder the terms: 0.5 + x = -1.5 Solving 0.5 + x = -1.5 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 = -1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.5 + -0.5 x = -1.5 + -0.5 Combine like terms: -1.5 + -0.5 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -2}Solution
x = {0, 1, -2}
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