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Simplifying x3 + 5x2 + 3x = 0 Reorder the terms: 3x + 5x2 + x3 = 0 Solving 3x + 5x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 5x + 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 '(3 + 5x + x2)' equal to zero and attempt to solve: Simplifying 3 + 5x + x2 = 0 Solving 3 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x + x2 = 0 + -3 5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 5x + x2 = -3 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -3 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + 5x + x2 = 3.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 2.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 2.5 = 1.802775638 Simplifying x + 2.5 = 1.802775638 Reorder the terms: 2.5 + x = 1.802775638 Solving 2.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.802775638 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.802775638 + -2.5 x = 1.802775638 + -2.5 Combine like terms: 1.802775638 + -2.5 = -0.697224362 x = -0.697224362 Simplifying x = -0.697224362Subproblem 2
x + 2.5 = -1.802775638 Simplifying x + 2.5 = -1.802775638 Reorder the terms: 2.5 + x = -1.802775638 Solving 2.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.802775638 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.802775638 + -2.5 x = -1.802775638 + -2.5 Combine like terms: -1.802775638 + -2.5 = -4.302775638 x = -4.302775638 Simplifying x = -4.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.697224362, -4.302775638}Solution
x = {0, -0.697224362, -4.302775638}
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