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Simplifying 3x3 + -12x2 + 5x = 0 Reorder the terms: 5x + -12x2 + 3x3 = 0 Solving 5x + -12x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + -12x + 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 '(5 + -12x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + -12x + 3x2 = 0 Solving 5 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -4x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -4x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -4x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + -1.666666667 -4x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -4x + x2 = -1.666666667 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 = -1.666666667 + 4 Reorder the terms: 4 + -4x + x2 = -1.666666667 + 4 Combine like terms: -1.666666667 + 4 = 2.333333333 4 + -4x + x2 = 2.333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -2) equal to 1.527525232 and -1.527525232.Subproblem 1
x + -2 = 1.527525232 Simplifying x + -2 = 1.527525232 Reorder the terms: -2 + x = 1.527525232 Solving -2 + x = 1.527525232 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 = 1.527525232 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.527525232 + 2 x = 1.527525232 + 2 Combine like terms: 1.527525232 + 2 = 3.527525232 x = 3.527525232 Simplifying x = 3.527525232Subproblem 2
x + -2 = -1.527525232 Simplifying x + -2 = -1.527525232 Reorder the terms: -2 + x = -1.527525232 Solving -2 + x = -1.527525232 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 = -1.527525232 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.527525232 + 2 x = -1.527525232 + 2 Combine like terms: -1.527525232 + 2 = 0.472474768 x = 0.472474768 Simplifying x = 0.472474768Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.527525232, 0.472474768}Solution
x = {0, 3.527525232, 0.472474768}
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