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Simplifying 3x(x2 + -4x + -4) + -2x(x2 + -2x + 3) = 0 Reorder the terms: 3x(-4 + -4x + x2) + -2x(x2 + -2x + 3) = 0 (-4 * 3x + -4x * 3x + x2 * 3x) + -2x(x2 + -2x + 3) = 0 (-12x + -12x2 + 3x3) + -2x(x2 + -2x + 3) = 0 Reorder the terms: -12x + -12x2 + 3x3 + -2x(3 + -2x + x2) = 0 -12x + -12x2 + 3x3 + (3 * -2x + -2x * -2x + x2 * -2x) = 0 -12x + -12x2 + 3x3 + (-6x + 4x2 + -2x3) = 0 Reorder the terms: -12x + -6x + -12x2 + 4x2 + 3x3 + -2x3 = 0 Combine like terms: -12x + -6x = -18x -18x + -12x2 + 4x2 + 3x3 + -2x3 = 0 Combine like terms: -12x2 + 4x2 = -8x2 -18x + -8x2 + 3x3 + -2x3 = 0 Combine like terms: 3x3 + -2x3 = 1x3 -18x + -8x2 + 1x3 = 0 Solving -18x + -8x2 + 1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-18 + -8x + x2) = 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 '(-18 + -8x + x2)' equal to zero and attempt to solve: Simplifying -18 + -8x + x2 = 0 Solving -18 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -8x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -8x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -8x + x2 = 0 + 18 -8x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -8x + x2 = 18 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 18 + 16 Reorder the terms: 16 + -8x + x2 = 18 + 16 Combine like terms: 18 + 16 = 34 16 + -8x + x2 = 34 Factor a perfect square on the left side: (x + -4)(x + -4) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -4) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -4 = 5.830951895 Simplifying x + -4 = 5.830951895 Reorder the terms: -4 + x = 5.830951895 Solving -4 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.830951895 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.830951895 + 4 x = 5.830951895 + 4 Combine like terms: 5.830951895 + 4 = 9.830951895 x = 9.830951895 Simplifying x = 9.830951895Subproblem 2
x + -4 = -5.830951895 Simplifying x + -4 = -5.830951895 Reorder the terms: -4 + x = -5.830951895 Solving -4 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.830951895 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.830951895 + 4 x = -5.830951895 + 4 Combine like terms: -5.830951895 + 4 = -1.830951895 x = -1.830951895 Simplifying x = -1.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.830951895, -1.830951895}Solution
x = {0, 9.830951895, -1.830951895}
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