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Simplifying 5x3 + 20x2 + -1x = 0 Reorder the terms: -1x + 20x2 + 5x3 = 0 Solving -1x + 20x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 20x + 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 '(-1 + 20x + 5x2)' equal to zero and attempt to solve: Simplifying -1 + 20x + 5x2 = 0 Solving -1 + 20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 4x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 4x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 4x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 4x + x2 = 0 + 0.2 4x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 4x + x2 = 0.2 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 0.2 + 4 Reorder the terms: 4 + 4x + x2 = 0.2 + 4 Combine like terms: 0.2 + 4 = 4.2 4 + 4x + x2 = 4.2 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.2 Calculate the square root of the right side: 2.049390153 Break this problem into two subproblems by setting (x + 2) equal to 2.049390153 and -2.049390153.Subproblem 1
x + 2 = 2.049390153 Simplifying x + 2 = 2.049390153 Reorder the terms: 2 + x = 2.049390153 Solving 2 + x = 2.049390153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.049390153 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.049390153 + -2 x = 2.049390153 + -2 Combine like terms: 2.049390153 + -2 = 0.049390153 x = 0.049390153 Simplifying x = 0.049390153Subproblem 2
x + 2 = -2.049390153 Simplifying x + 2 = -2.049390153 Reorder the terms: 2 + x = -2.049390153 Solving 2 + x = -2.049390153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.049390153 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.049390153 + -2 x = -2.049390153 + -2 Combine like terms: -2.049390153 + -2 = -4.049390153 x = -4.049390153 Simplifying x = -4.049390153Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.049390153, -4.049390153}Solution
x = {0, 0.049390153, -4.049390153}
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