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Simplifying 2x3 + 14x2 + 18x = 0 Reorder the terms: 18x + 14x2 + 2x3 = 0 Solving 18x + 14x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(9 + 7x + x2) = 0 Ignore the factor 2.Subproblem 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 '(9 + 7x + x2)' equal to zero and attempt to solve: Simplifying 9 + 7x + x2 = 0 Solving 9 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 7x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 7x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7x + x2 = 0 + -9 7x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 7x + x2 = -9 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -9 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -9 + 12.25 Combine like terms: -9 + 12.25 = 3.25 12.25 + 7x + x2 = 3.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 3.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 3.5 = 1.802775638 Simplifying x + 3.5 = 1.802775638 Reorder the terms: 3.5 + x = 1.802775638 Solving 3.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 1.802775638 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.802775638 + -3.5 x = 1.802775638 + -3.5 Combine like terms: 1.802775638 + -3.5 = -1.697224362 x = -1.697224362 Simplifying x = -1.697224362Subproblem 2
x + 3.5 = -1.802775638 Simplifying x + 3.5 = -1.802775638 Reorder the terms: 3.5 + x = -1.802775638 Solving 3.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -1.802775638 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.802775638 + -3.5 x = -1.802775638 + -3.5 Combine like terms: -1.802775638 + -3.5 = -5.302775638 x = -5.302775638 Simplifying x = -5.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.697224362, -5.302775638}Solution
x = {0, -1.697224362, -5.302775638}
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