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Simplifying 9x3 + 21x2 + 1x = 0 Reorder the terms: 1x + 21x2 + 9x3 = 0 Solving 1x + 21x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 21x + 9x2) = 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 '(1 + 21x + 9x2)' equal to zero and attempt to solve: Simplifying 1 + 21x + 9x2 = 0 Solving 1 + 21x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 2.333333333x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 2.333333333x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 2.333333333x + x2 = 0 + -0.1111111111 2.333333333x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 2.333333333x + x2 = -0.1111111111 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = -0.1111111111 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -0.1111111111 + 1.361111112 Combine like terms: -0.1111111111 + 1.361111112 = 1.2500000009 1.361111112 + 2.333333333x + x2 = 1.2500000009 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 1.2500000009 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 1.166666667 = 1.118033989 Simplifying x + 1.166666667 = 1.118033989 Reorder the terms: 1.166666667 + x = 1.118033989 Solving 1.166666667 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 1.118033989 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.118033989 + -1.166666667 x = 1.118033989 + -1.166666667 Combine like terms: 1.118033989 + -1.166666667 = -0.048632678 x = -0.048632678 Simplifying x = -0.048632678Subproblem 2
x + 1.166666667 = -1.118033989 Simplifying x + 1.166666667 = -1.118033989 Reorder the terms: 1.166666667 + x = -1.118033989 Solving 1.166666667 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -1.118033989 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.118033989 + -1.166666667 x = -1.118033989 + -1.166666667 Combine like terms: -1.118033989 + -1.166666667 = -2.284700656 x = -2.284700656 Simplifying x = -2.284700656Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.048632678, -2.284700656}Solution
x = {0, -0.048632678, -2.284700656}
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