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Simplifying 3x3 + 20x2 + 21x = 0 Reorder the terms: 21x + 20x2 + 3x3 = 0 Solving 21x + 20x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(21 + 20x + 3x2) = 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 '(21 + 20x + 3x2)' equal to zero and attempt to solve: Simplifying 21 + 20x + 3x2 = 0 Solving 21 + 20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6.666666667x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 6.666666667x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6.666666667x + x2 = 0 + -7 6.666666667x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 6.666666667x + x2 = -7 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = -7 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = -7 + 11.11111112 Combine like terms: -7 + 11.11111112 = 4.11111112 11.11111112 + 6.666666667x + x2 = 4.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 4.11111112 Calculate the square root of the right side: 2.027587512 Break this problem into two subproblems by setting (x + 3.333333334) equal to 2.027587512 and -2.027587512.Subproblem 1
x + 3.333333334 = 2.027587512 Simplifying x + 3.333333334 = 2.027587512 Reorder the terms: 3.333333334 + x = 2.027587512 Solving 3.333333334 + x = 2.027587512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 2.027587512 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 2.027587512 + -3.333333334 x = 2.027587512 + -3.333333334 Combine like terms: 2.027587512 + -3.333333334 = -1.305745822 x = -1.305745822 Simplifying x = -1.305745822Subproblem 2
x + 3.333333334 = -2.027587512 Simplifying x + 3.333333334 = -2.027587512 Reorder the terms: 3.333333334 + x = -2.027587512 Solving 3.333333334 + x = -2.027587512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -2.027587512 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -2.027587512 + -3.333333334 x = -2.027587512 + -3.333333334 Combine like terms: -2.027587512 + -3.333333334 = -5.360920846 x = -5.360920846 Simplifying x = -5.360920846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.305745822, -5.360920846}Solution
x = {0, -1.305745822, -5.360920846}
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