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Simplifying 5x3 + 18x2 + 15x = 0 Reorder the terms: 15x + 18x2 + 5x3 = 0 Solving 15x + 18x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(15 + 18x + 5x2) = 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 '(15 + 18x + 5x2)' equal to zero and attempt to solve: Simplifying 15 + 18x + 5x2 = 0 Solving 15 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + 3.6x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.6x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3.6x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.6x + x2 = 0 + -3 3.6x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.6x + x2 = -3 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = -3 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = -3 + 3.24 Combine like terms: -3 + 3.24 = 0.24 3.24 + 3.6x + x2 = 0.24 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + 1.8) equal to 0.489897949 and -0.489897949.Subproblem 1
x + 1.8 = 0.489897949 Simplifying x + 1.8 = 0.489897949 Reorder the terms: 1.8 + x = 0.489897949 Solving 1.8 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 0.489897949 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 0.489897949 + -1.8 x = 0.489897949 + -1.8 Combine like terms: 0.489897949 + -1.8 = -1.310102051 x = -1.310102051 Simplifying x = -1.310102051Subproblem 2
x + 1.8 = -0.489897949 Simplifying x + 1.8 = -0.489897949 Reorder the terms: 1.8 + x = -0.489897949 Solving 1.8 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -0.489897949 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -0.489897949 + -1.8 x = -0.489897949 + -1.8 Combine like terms: -0.489897949 + -1.8 = -2.289897949 x = -2.289897949 Simplifying x = -2.289897949Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.310102051, -2.289897949}Solution
x = {0, -1.310102051, -2.289897949}
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