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Simplifying 5x3 + 21x2 + 3x = 0 Reorder the terms: 3x + 21x2 + 5x3 = 0 Solving 3x + 21x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 21x + 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 '(3 + 21x + 5x2)' equal to zero and attempt to solve: Simplifying 3 + 21x + 5x2 = 0 Solving 3 + 21x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 4.2x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 4.2x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 4.2x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 4.2x + x2 = 0 + -0.6 4.2x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 4.2x + x2 = -0.6 The x term is 4.2x. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2x + 4.41 + x2 = -0.6 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = -0.6 + 4.41 Combine like terms: -0.6 + 4.41 = 3.81 4.41 + 4.2x + x2 = 3.81 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 3.81 Calculate the square root of the right side: 1.95192213 Break this problem into two subproblems by setting (x + 2.1) equal to 1.95192213 and -1.95192213.Subproblem 1
x + 2.1 = 1.95192213 Simplifying x + 2.1 = 1.95192213 Reorder the terms: 2.1 + x = 1.95192213 Solving 2.1 + x = 1.95192213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 1.95192213 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 1.95192213 + -2.1 x = 1.95192213 + -2.1 Combine like terms: 1.95192213 + -2.1 = -0.14807787 x = -0.14807787 Simplifying x = -0.14807787Subproblem 2
x + 2.1 = -1.95192213 Simplifying x + 2.1 = -1.95192213 Reorder the terms: 2.1 + x = -1.95192213 Solving 2.1 + x = -1.95192213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -1.95192213 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -1.95192213 + -2.1 x = -1.95192213 + -2.1 Combine like terms: -1.95192213 + -2.1 = -4.05192213 x = -4.05192213 Simplifying x = -4.05192213Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.14807787, -4.05192213}Solution
x = {0, -0.14807787, -4.05192213}
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