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Simplifying 3x3 + 13x2 + 3x = 0 Reorder the terms: 3x + 13x2 + 3x3 = 0 Solving 3x + 13x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 13x + 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 '(3 + 13x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + 13x + 3x2 = 0 Solving 3 + 13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 4.333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.333333333x + x2 = 0 + -1 4.333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.333333333x + x2 = -1 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = -1 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = -1 + 4.694444446 Combine like terms: -1 + 4.694444446 = 3.694444446 4.694444446 + 4.333333333x + x2 = 3.694444446 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 3.694444446 Calculate the square root of the right side: 1.922093766 Break this problem into two subproblems by setting (x + 2.166666667) equal to 1.922093766 and -1.922093766.Subproblem 1
x + 2.166666667 = 1.922093766 Simplifying x + 2.166666667 = 1.922093766 Reorder the terms: 2.166666667 + x = 1.922093766 Solving 2.166666667 + x = 1.922093766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 1.922093766 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 1.922093766 + -2.166666667 x = 1.922093766 + -2.166666667 Combine like terms: 1.922093766 + -2.166666667 = -0.244572901 x = -0.244572901 Simplifying x = -0.244572901Subproblem 2
x + 2.166666667 = -1.922093766 Simplifying x + 2.166666667 = -1.922093766 Reorder the terms: 2.166666667 + x = -1.922093766 Solving 2.166666667 + x = -1.922093766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -1.922093766 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -1.922093766 + -2.166666667 x = -1.922093766 + -2.166666667 Combine like terms: -1.922093766 + -2.166666667 = -4.088760433 x = -4.088760433 Simplifying x = -4.088760433Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.244572901, -4.088760433}Solution
x = {0, -0.244572901, -4.088760433}
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