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Simplifying x3 + -15x2 + -600x = 0 Reorder the terms: -600x + -15x2 + x3 = 0 Solving -600x + -15x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-600 + -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 '(-600 + -15x + x2)' equal to zero and attempt to solve: Simplifying -600 + -15x + x2 = 0 Solving -600 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + -15x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -15x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -15x + x2 = 0 + 600 -15x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -15x + x2 = 600 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 = 600 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 600 + 56.25 Combine like terms: 600 + 56.25 = 656.25 56.25 + -15x + x2 = 656.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 656.25 Calculate the square root of the right side: 25.617376915 Break this problem into two subproblems by setting (x + -7.5) equal to 25.617376915 and -25.617376915.Subproblem 1
x + -7.5 = 25.617376915 Simplifying x + -7.5 = 25.617376915 Reorder the terms: -7.5 + x = 25.617376915 Solving -7.5 + x = 25.617376915 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 = 25.617376915 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 25.617376915 + 7.5 x = 25.617376915 + 7.5 Combine like terms: 25.617376915 + 7.5 = 33.117376915 x = 33.117376915 Simplifying x = 33.117376915Subproblem 2
x + -7.5 = -25.617376915 Simplifying x + -7.5 = -25.617376915 Reorder the terms: -7.5 + x = -25.617376915 Solving -7.5 + x = -25.617376915 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 = -25.617376915 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -25.617376915 + 7.5 x = -25.617376915 + 7.5 Combine like terms: -25.617376915 + 7.5 = -18.117376915 x = -18.117376915 Simplifying x = -18.117376915Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.117376915, -18.117376915}Solution
x = {0, 33.117376915, -18.117376915}
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