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Simplifying x4 + 8x3 + 6x2 = 0 Reorder the terms: 6x2 + 8x3 + x4 = 0 Solving 6x2 + 8x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(6 + 8x + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(6 + 8x + x2)' equal to zero and attempt to solve: Simplifying 6 + 8x + x2 = 0 Solving 6 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 8x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 8x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 8x + x2 = 0 + -6 8x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 8x + x2 = -6 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 = -6 + 16 Reorder the terms: 16 + 8x + x2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + 8x + x2 = 10 Factor a perfect square on the left side: (x + 4)(x + 4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 4) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 4 = 3.16227766 Simplifying x + 4 = 3.16227766 Reorder the terms: 4 + x = 3.16227766 Solving 4 + x = 3.16227766 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 = 3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.16227766 + -4 x = 3.16227766 + -4 Combine like terms: 3.16227766 + -4 = -0.83772234 x = -0.83772234 Simplifying x = -0.83772234Subproblem 2
x + 4 = -3.16227766 Simplifying x + 4 = -3.16227766 Reorder the terms: 4 + x = -3.16227766 Solving 4 + x = -3.16227766 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 = -3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.16227766 + -4 x = -3.16227766 + -4 Combine like terms: -3.16227766 + -4 = -7.16227766 x = -7.16227766 Simplifying x = -7.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.83772234, -7.16227766}Solution
x = {0, -0.83772234, -7.16227766}
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