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Simplifying 6x3 + 17x2 + 4x = 0 Reorder the terms: 4x + 17x2 + 6x3 = 0 Solving 4x + 17x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + 17x + 6x2) = 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 '(4 + 17x + 6x2)' equal to zero and attempt to solve: Simplifying 4 + 17x + 6x2 = 0 Solving 4 + 17x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + 2.833333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 2.833333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 2.833333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 2.833333333x + x2 = 0 + -0.6666666667 2.833333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 2.833333333x + x2 = -0.6666666667 The x term is 2.833333333x. Take half its coefficient (1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. 2.833333333x + 2.006944445 + x2 = -0.6666666667 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333x + x2 = -0.6666666667 + 2.006944445 Combine like terms: -0.6666666667 + 2.006944445 = 1.3402777783 2.006944445 + 2.833333333x + x2 = 1.3402777783 Factor a perfect square on the left side: (x + 1.416666667)(x + 1.416666667) = 1.3402777783 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x + 1.416666667) equal to 1.157703666 and -1.157703666.Subproblem 1
x + 1.416666667 = 1.157703666 Simplifying x + 1.416666667 = 1.157703666 Reorder the terms: 1.416666667 + x = 1.157703666 Solving 1.416666667 + x = 1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = 1.157703666 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = 1.157703666 + -1.416666667 x = 1.157703666 + -1.416666667 Combine like terms: 1.157703666 + -1.416666667 = -0.258963001 x = -0.258963001 Simplifying x = -0.258963001Subproblem 2
x + 1.416666667 = -1.157703666 Simplifying x + 1.416666667 = -1.157703666 Reorder the terms: 1.416666667 + x = -1.157703666 Solving 1.416666667 + x = -1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = -1.157703666 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = -1.157703666 + -1.416666667 x = -1.157703666 + -1.416666667 Combine like terms: -1.157703666 + -1.416666667 = -2.574370333 x = -2.574370333 Simplifying x = -2.574370333Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.258963001, -2.574370333}Solution
x = {0, -0.258963001, -2.574370333}
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