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Simplifying 3x + -4 * 2(x + -6) * 4(x + 1) * x + 3 * 6x = 0 Reorder the terms: 3x + -4 * 2(-6 + x) * 4(x + 1) * x + 3 * 6x = 0 Reorder the terms: 3x + -4 * 2(-6 + x) * 4(1 + x) * x + 3 * 6x = 0 Reorder the terms for easier multiplication: 3x + -4 * 2 * 4x(-6 + x)(1 + x) + 3 * 6x = 0 Multiply -4 * 2 3x + -8 * 4x(-6 + x)(1 + x) + 3 * 6x = 0 Multiply -8 * 4 3x + -32x(-6 + x)(1 + x) + 3 * 6x = 0 Multiply (-6 + x) * (1 + x) 3x + -32x(-6(1 + x) + x(1 + x)) + 3 * 6x = 0 3x + -32x((1 * -6 + x * -6) + x(1 + x)) + 3 * 6x = 0 3x + -32x((-6 + -6x) + x(1 + x)) + 3 * 6x = 0 3x + -32x(-6 + -6x + (1 * x + x * x)) + 3 * 6x = 0 3x + -32x(-6 + -6x + (1x + x2)) + 3 * 6x = 0 Combine like terms: -6x + 1x = -5x 3x + -32x(-6 + -5x + x2) + 3 * 6x = 0 3x + (-6 * -32x + -5x * -32x + x2 * -32x) + 3 * 6x = 0 3x + (192x + 160x2 + -32x3) + 3 * 6x = 0 Multiply 3 * 6 3x + 192x + 160x2 + -32x3 + 18x = 0 Reorder the terms: 3x + 192x + 18x + 160x2 + -32x3 = 0 Combine like terms: 3x + 192x = 195x 195x + 18x + 160x2 + -32x3 = 0 Combine like terms: 195x + 18x = 213x 213x + 160x2 + -32x3 = 0 Solving 213x + 160x2 + -32x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(213 + 160x + -32x2) = 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 '(213 + 160x + -32x2)' equal to zero and attempt to solve: Simplifying 213 + 160x + -32x2 = 0 Solving 213 + 160x + -32x2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -6.65625 + -5x + x2 = 0 Move the constant term to the right: Add '6.65625' to each side of the equation. -6.65625 + -5x + 6.65625 + x2 = 0 + 6.65625 Reorder the terms: -6.65625 + 6.65625 + -5x + x2 = 0 + 6.65625 Combine like terms: -6.65625 + 6.65625 = 0.00000 0.00000 + -5x + x2 = 0 + 6.65625 -5x + x2 = 0 + 6.65625 Combine like terms: 0 + 6.65625 = 6.65625 -5x + x2 = 6.65625 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 = 6.65625 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 6.65625 + 6.25 Combine like terms: 6.65625 + 6.25 = 12.90625 6.25 + -5x + x2 = 12.90625 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 12.90625 Calculate the square root of the right side: 3.592526966 Break this problem into two subproblems by setting (x + -2.5) equal to 3.592526966 and -3.592526966.Subproblem 1
x + -2.5 = 3.592526966 Simplifying x + -2.5 = 3.592526966 Reorder the terms: -2.5 + x = 3.592526966 Solving -2.5 + x = 3.592526966 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 = 3.592526966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.592526966 + 2.5 x = 3.592526966 + 2.5 Combine like terms: 3.592526966 + 2.5 = 6.092526966 x = 6.092526966 Simplifying x = 6.092526966Subproblem 2
x + -2.5 = -3.592526966 Simplifying x + -2.5 = -3.592526966 Reorder the terms: -2.5 + x = -3.592526966 Solving -2.5 + x = -3.592526966 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 = -3.592526966 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.592526966 + 2.5 x = -3.592526966 + 2.5 Combine like terms: -3.592526966 + 2.5 = -1.092526966 x = -1.092526966 Simplifying x = -1.092526966Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.092526966, -1.092526966}Solution
x = {0, 6.092526966, -1.092526966}
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