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Simplifying 4x3 + 42x2 + 30x = 0 Reorder the terms: 30x + 42x2 + 4x3 = 0 Solving 30x + 42x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(15 + 21x + 2x2) = 0 Ignore the factor 2.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 '(15 + 21x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + 21x + 2x2 = 0 Solving 15 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 10.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 10.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 10.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 10.5x + x2 = 0 + -7.5 10.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 10.5x + x2 = -7.5 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = -7.5 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = -7.5 + 27.5625 Combine like terms: -7.5 + 27.5625 = 20.0625 27.5625 + 10.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + 5.25) equal to 4.479118217 and -4.479118217.Subproblem 1
x + 5.25 = 4.479118217 Simplifying x + 5.25 = 4.479118217 Reorder the terms: 5.25 + x = 4.479118217 Solving 5.25 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 4.479118217 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 4.479118217 + -5.25 x = 4.479118217 + -5.25 Combine like terms: 4.479118217 + -5.25 = -0.770881783 x = -0.770881783 Simplifying x = -0.770881783Subproblem 2
x + 5.25 = -4.479118217 Simplifying x + 5.25 = -4.479118217 Reorder the terms: 5.25 + x = -4.479118217 Solving 5.25 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -4.479118217 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -4.479118217 + -5.25 x = -4.479118217 + -5.25 Combine like terms: -4.479118217 + -5.25 = -9.729118217 x = -9.729118217 Simplifying x = -9.729118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.770881783, -9.729118217}Solution
x = {0, -0.770881783, -9.729118217}
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