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Simplifying x3 + 15x2 + 35x = 0 Reorder the terms: 35x + 15x2 + x3 = 0 Solving 35x + 15x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(35 + 15x + 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 '(35 + 15x + x2)' equal to zero and attempt to solve: Simplifying 35 + 15x + x2 = 0 Solving 35 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 15x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 15x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 15x + x2 = 0 + -35 15x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 15x + x2 = -35 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -35 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -35 + 56.25 Combine like terms: -35 + 56.25 = 21.25 56.25 + 15x + x2 = 21.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + 7.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + 7.5 = 4.609772229 Simplifying x + 7.5 = 4.609772229 Reorder the terms: 7.5 + x = 4.609772229 Solving 7.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 4.609772229 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 4.609772229 + -7.5 x = 4.609772229 + -7.5 Combine like terms: 4.609772229 + -7.5 = -2.890227771 x = -2.890227771 Simplifying x = -2.890227771Subproblem 2
x + 7.5 = -4.609772229 Simplifying x + 7.5 = -4.609772229 Reorder the terms: 7.5 + x = -4.609772229 Solving 7.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -4.609772229 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -4.609772229 + -7.5 x = -4.609772229 + -7.5 Combine like terms: -4.609772229 + -7.5 = -12.109772229 x = -12.109772229 Simplifying x = -12.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.890227771, -12.109772229}Solution
x = {0, -2.890227771, -12.109772229}
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