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Simplifying 6x3 + 30x2 + -16x = 0 Reorder the terms: -16x + 30x2 + 6x3 = 0 Solving -16x + 30x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-8 + 15x + 3x2) = 0 Ignore the factor 2.Subproblem 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 '(-8 + 15x + 3x2)' equal to zero and attempt to solve: Simplifying -8 + 15x + 3x2 = 0 Solving -8 + 15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + 5x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 5x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 5x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 5x + x2 = 0 + 2.666666667 5x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 5x + x2 = 2.666666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 2.666666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2.666666667 + 6.25 Combine like terms: 2.666666667 + 6.25 = 8.916666667 6.25 + 5x + x2 = 8.916666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 8.916666667 Calculate the square root of the right side: 2.986078811 Break this problem into two subproblems by setting (x + 2.5) equal to 2.986078811 and -2.986078811.Subproblem 1
x + 2.5 = 2.986078811 Simplifying x + 2.5 = 2.986078811 Reorder the terms: 2.5 + x = 2.986078811 Solving 2.5 + x = 2.986078811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.986078811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.986078811 + -2.5 x = 2.986078811 + -2.5 Combine like terms: 2.986078811 + -2.5 = 0.486078811 x = 0.486078811 Simplifying x = 0.486078811Subproblem 2
x + 2.5 = -2.986078811 Simplifying x + 2.5 = -2.986078811 Reorder the terms: 2.5 + x = -2.986078811 Solving 2.5 + x = -2.986078811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.986078811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.986078811 + -2.5 x = -2.986078811 + -2.5 Combine like terms: -2.986078811 + -2.5 = -5.486078811 x = -5.486078811 Simplifying x = -5.486078811Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.486078811, -5.486078811}Solution
x = {0, 0.486078811, -5.486078811}
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