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Simplifying x3 + 20x2 + 45x = 0 Reorder the terms: 45x + 20x2 + x3 = 0 Solving 45x + 20x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(45 + 20x + 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 '(45 + 20x + x2)' equal to zero and attempt to solve: Simplifying 45 + 20x + x2 = 0 Solving 45 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 20x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 20x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 20x + x2 = 0 + -45 20x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 20x + x2 = -45 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -45 + 100 Reorder the terms: 100 + 20x + x2 = -45 + 100 Combine like terms: -45 + 100 = 55 100 + 20x + x2 = 55 Factor a perfect square on the left side: (x + 10)(x + 10) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + 10) equal to 7.416198487 and -7.416198487.Subproblem 1
x + 10 = 7.416198487 Simplifying x + 10 = 7.416198487 Reorder the terms: 10 + x = 7.416198487 Solving 10 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 7.416198487 + -10 Combine like terms: 10 + -10 = 0 0 + x = 7.416198487 + -10 x = 7.416198487 + -10 Combine like terms: 7.416198487 + -10 = -2.583801513 x = -2.583801513 Simplifying x = -2.583801513Subproblem 2
x + 10 = -7.416198487 Simplifying x + 10 = -7.416198487 Reorder the terms: 10 + x = -7.416198487 Solving 10 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -7.416198487 + -10 Combine like terms: 10 + -10 = 0 0 + x = -7.416198487 + -10 x = -7.416198487 + -10 Combine like terms: -7.416198487 + -10 = -17.416198487 x = -17.416198487 Simplifying x = -17.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.583801513, -17.416198487}Solution
x = {0, -2.583801513, -17.416198487}
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