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Simplifying 12X3 + 3X2 + -24X + -6X = 0 Reorder the terms: -24X + -6X + 3X2 + 12X3 = 0 Combine like terms: -24X + -6X = -30X -30X + 3X2 + 12X3 = 0 Solving -30X + 3X2 + 12X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '3X'. 3X(-10 + X + 4X2) = 0 Ignore the factor 3.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 '(-10 + X + 4X2)' equal to zero and attempt to solve: Simplifying -10 + X + 4X2 = 0 Solving -10 + X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + 0.25X + X2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.25X + 2.5 + X2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.25X + X2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.25X + X2 = 0 + 2.5 0.25X + X2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.25X + X2 = 2.5 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25X + 0.25 + X2 = 2.5 + 0.25 Reorder the terms: 0.25 + 0.25X + X2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 0.25 + 0.25X + X2 = 2.75 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (X + 0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
X + 0.5 = 1.658312395 Simplifying X + 0.5 = 1.658312395 Reorder the terms: 0.5 + X = 1.658312395 Solving 0.5 + X = 1.658312395 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 1.658312395 + -0.5 X = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 X = 1.158312395 Simplifying X = 1.158312395Subproblem 2
X + 0.5 = -1.658312395 Simplifying X + 0.5 = -1.658312395 Reorder the terms: 0.5 + X = -1.658312395 Solving 0.5 + X = -1.658312395 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -1.658312395 + -0.5 X = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 X = -2.158312395 Simplifying X = -2.158312395Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.158312395, -2.158312395}Solution
X = {0, 1.158312395, -2.158312395}
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