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Simplifying 9x3 + 36x2 + 21x = 0 Reorder the terms: 21x + 36x2 + 9x3 = 0 Solving 21x + 36x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(7 + 12x + 3x2) = 0 Ignore the factor 3.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 '(7 + 12x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + 12x + 3x2 = 0 Solving 7 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 4x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 4x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 4x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 4x + x2 = 0 + -2.333333333 4x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 4x + x2 = -2.333333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2.333333333 + 4 Reorder the terms: 4 + 4x + x2 = -2.333333333 + 4 Combine like terms: -2.333333333 + 4 = 1.666666667 4 + 4x + x2 = 1.666666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (x + 2) equal to 1.290994449 and -1.290994449.Subproblem 1
x + 2 = 1.290994449 Simplifying x + 2 = 1.290994449 Reorder the terms: 2 + x = 1.290994449 Solving 2 + x = 1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.290994449 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.290994449 + -2 x = 1.290994449 + -2 Combine like terms: 1.290994449 + -2 = -0.709005551 x = -0.709005551 Simplifying x = -0.709005551Subproblem 2
x + 2 = -1.290994449 Simplifying x + 2 = -1.290994449 Reorder the terms: 2 + x = -1.290994449 Solving 2 + x = -1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.290994449 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.290994449 + -2 x = -1.290994449 + -2 Combine like terms: -1.290994449 + -2 = -3.290994449 x = -3.290994449 Simplifying x = -3.290994449Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.709005551, -3.290994449}Solution
x = {0, -0.709005551, -3.290994449}
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