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Simplifying 5x3 + 21x2 + -12x = 0 Reorder the terms: -12x + 21x2 + 5x3 = 0 Solving -12x + 21x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + 21x + 5x2) = 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 '(-12 + 21x + 5x2)' equal to zero and attempt to solve: Simplifying -12 + 21x + 5x2 = 0 Solving -12 + 21x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 4.2x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 4.2x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 4.2x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 4.2x + x2 = 0 + 2.4 4.2x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 4.2x + x2 = 2.4 The x term is 4.2x. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2x + 4.41 + x2 = 2.4 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 2.4 + 4.41 Combine like terms: 2.4 + 4.41 = 6.81 4.41 + 4.2x + x2 = 6.81 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 6.81 Calculate the square root of the right side: 2.60959767 Break this problem into two subproblems by setting (x + 2.1) equal to 2.60959767 and -2.60959767.Subproblem 1
x + 2.1 = 2.60959767 Simplifying x + 2.1 = 2.60959767 Reorder the terms: 2.1 + x = 2.60959767 Solving 2.1 + x = 2.60959767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 2.60959767 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 2.60959767 + -2.1 x = 2.60959767 + -2.1 Combine like terms: 2.60959767 + -2.1 = 0.50959767 x = 0.50959767 Simplifying x = 0.50959767Subproblem 2
x + 2.1 = -2.60959767 Simplifying x + 2.1 = -2.60959767 Reorder the terms: 2.1 + x = -2.60959767 Solving 2.1 + x = -2.60959767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -2.60959767 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -2.60959767 + -2.1 x = -2.60959767 + -2.1 Combine like terms: -2.60959767 + -2.1 = -4.70959767 x = -4.70959767 Simplifying x = -4.70959767Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.50959767, -4.70959767}Solution
x = {0, 0.50959767, -4.70959767}
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