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Simplifying 3x3 + 24x2 + 15x = 0 Reorder the terms: 15x + 24x2 + 3x3 = 0 Solving 15x + 24x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(5 + 8x + x2) = 0 Ignore the factor 3.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 '(5 + 8x + x2)' equal to zero and attempt to solve: Simplifying 5 + 8x + x2 = 0 Solving 5 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 8x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 8x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8x + x2 = 0 + -5 8x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 8x + x2 = -5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -5 + 16 Reorder the terms: 16 + 8x + x2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + 8x + x2 = 11 Factor a perfect square on the left side: (x + 4)(x + 4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 4) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 4 = 3.31662479 Simplifying x + 4 = 3.31662479 Reorder the terms: 4 + x = 3.31662479 Solving 4 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.31662479 + -4 x = 3.31662479 + -4 Combine like terms: 3.31662479 + -4 = -0.68337521 x = -0.68337521 Simplifying x = -0.68337521Subproblem 2
x + 4 = -3.31662479 Simplifying x + 4 = -3.31662479 Reorder the terms: 4 + x = -3.31662479 Solving 4 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.31662479 + -4 x = -3.31662479 + -4 Combine like terms: -3.31662479 + -4 = -7.31662479 x = -7.31662479 Simplifying x = -7.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.68337521, -7.31662479}Solution
x = {0, -0.68337521, -7.31662479}
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