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Simplifying 4x3 + 16x2 + -24x = 0 Reorder the terms: -24x + 16x2 + 4x3 = 0 Solving -24x + 16x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-6 + 4x + x2) = 0 Ignore the factor 4.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 '(-6 + 4x + x2)' equal to zero and attempt to solve: Simplifying -6 + 4x + x2 = 0 Solving -6 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4x + x2 = 0 + 6 4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 4x + x2 = 6 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 6 + 4 Reorder the terms: 4 + 4x + x2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + 4x + x2 = 10 Factor a perfect square on the left side: (x + 2)(x + 2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 2) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 2 = 3.16227766 Simplifying x + 2 = 3.16227766 Reorder the terms: 2 + x = 3.16227766 Solving 2 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.16227766 + -2 x = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 x = 1.16227766 Simplifying x = 1.16227766Subproblem 2
x + 2 = -3.16227766 Simplifying x + 2 = -3.16227766 Reorder the terms: 2 + x = -3.16227766 Solving 2 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.16227766 + -2 x = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 x = -5.16227766 Simplifying x = -5.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.16227766, -5.16227766}Solution
x = {0, 1.16227766, -5.16227766}
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