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Simplifying 20x3 + -24x2 + -6x = 0 Reorder the terms: -6x + -24x2 + 20x3 = 0 Solving -6x + -24x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + -12x + 10x2) = 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 '(-3 + -12x + 10x2)' equal to zero and attempt to solve: Simplifying -3 + -12x + 10x2 = 0 Solving -3 + -12x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -1.2x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -1.2x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.2x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.2x + x2 = 0.0 + 0.3 -1.2x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -1.2x + x2 = 0.3 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.3 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.3 + 0.36 Combine like terms: 0.3 + 0.36 = 0.66 0.36 + -1.2x + x2 = 0.66 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.66 Calculate the square root of the right side: 0.81240384 Break this problem into two subproblems by setting (x + -0.6) equal to 0.81240384 and -0.81240384.Subproblem 1
x + -0.6 = 0.81240384 Simplifying x + -0.6 = 0.81240384 Reorder the terms: -0.6 + x = 0.81240384 Solving -0.6 + x = 0.81240384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.81240384 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.81240384 + 0.6 x = 0.81240384 + 0.6 Combine like terms: 0.81240384 + 0.6 = 1.41240384 x = 1.41240384 Simplifying x = 1.41240384Subproblem 2
x + -0.6 = -0.81240384 Simplifying x + -0.6 = -0.81240384 Reorder the terms: -0.6 + x = -0.81240384 Solving -0.6 + x = -0.81240384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.81240384 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.81240384 + 0.6 x = -0.81240384 + 0.6 Combine like terms: -0.81240384 + 0.6 = -0.21240384 x = -0.21240384 Simplifying x = -0.21240384Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.41240384, -0.21240384}Solution
x = {0, 1.41240384, -0.21240384}
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