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Simplifying x4 = 16x3 + -5x2 Reorder the terms: x4 = -5x2 + 16x3 Solving x4 = -5x2 + 16x3 Solving for variable 'x'. Reorder the terms: 5x2 + -16x3 + x4 = -5x2 + 16x3 + 5x2 + -16x3 Reorder the terms: 5x2 + -16x3 + x4 = -5x2 + 5x2 + 16x3 + -16x3 Combine like terms: -5x2 + 5x2 = 0 5x2 + -16x3 + x4 = 0 + 16x3 + -16x3 5x2 + -16x3 + x4 = 16x3 + -16x3 Combine like terms: 16x3 + -16x3 = 0 5x2 + -16x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(5 + -16x + 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 '(5 + -16x + x2)' equal to zero and attempt to solve: Simplifying 5 + -16x + x2 = 0 Solving 5 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -16x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -16x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -16x + x2 = 0 + -5 -16x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -16x + x2 = -5 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -5 + 64 Reorder the terms: 64 + -16x + x2 = -5 + 64 Combine like terms: -5 + 64 = 59 64 + -16x + x2 = 59 Factor a perfect square on the left side: (x + -8)(x + -8) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + -8) equal to 7.681145748 and -7.681145748.Subproblem 1
x + -8 = 7.681145748 Simplifying x + -8 = 7.681145748 Reorder the terms: -8 + x = 7.681145748 Solving -8 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.681145748 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.681145748 + 8 x = 7.681145748 + 8 Combine like terms: 7.681145748 + 8 = 15.681145748 x = 15.681145748 Simplifying x = 15.681145748Subproblem 2
x + -8 = -7.681145748 Simplifying x + -8 = -7.681145748 Reorder the terms: -8 + x = -7.681145748 Solving -8 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.681145748 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.681145748 + 8 x = -7.681145748 + 8 Combine like terms: -7.681145748 + 8 = 0.318854252 x = 0.318854252 Simplifying x = 0.318854252Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.681145748, 0.318854252}Solution
x = {0, 15.681145748, 0.318854252}
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