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Simplifying 20x3 + 48x2 + 24x = 0 Reorder the terms: 24x + 48x2 + 20x3 = 0 Solving 24x + 48x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(6 + 12x + 5x2) = 0 Ignore the factor 4.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 '(6 + 12x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 12x + 5x2 = 0 Solving 6 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 2.4x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 2.4x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 2.4x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 2.4x + x2 = 0 + -1.2 2.4x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 2.4x + x2 = -1.2 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = -1.2 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = -1.2 + 1.44 Combine like terms: -1.2 + 1.44 = 0.24 1.44 + 2.4x + x2 = 0.24 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + 1.2) equal to 0.489897949 and -0.489897949.Subproblem 1
x + 1.2 = 0.489897949 Simplifying x + 1.2 = 0.489897949 Reorder the terms: 1.2 + x = 0.489897949 Solving 1.2 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 0.489897949 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 0.489897949 + -1.2 x = 0.489897949 + -1.2 Combine like terms: 0.489897949 + -1.2 = -0.710102051 x = -0.710102051 Simplifying x = -0.710102051Subproblem 2
x + 1.2 = -0.489897949 Simplifying x + 1.2 = -0.489897949 Reorder the terms: 1.2 + x = -0.489897949 Solving 1.2 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -0.489897949 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -0.489897949 + -1.2 x = -0.489897949 + -1.2 Combine like terms: -0.489897949 + -1.2 = -1.689897949 x = -1.689897949 Simplifying x = -1.689897949Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.710102051, -1.689897949}Solution
x = {0, -0.710102051, -1.689897949}
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