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Simplifying -1x4 + 16x3 + -36x2 = 0 Reorder the terms: -36x2 + 16x3 + -1x4 = 0 Solving -36x2 + 16x3 + -1x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-36 + 16x + -1x2) = 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 '(-36 + 16x + -1x2)' equal to zero and attempt to solve: Simplifying -36 + 16x + -1x2 = 0 Solving -36 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -16x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -16x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -16x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -16x + x2 = 0 + -36 -16x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -16x + x2 = -36 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 = -36 + 64 Reorder the terms: 64 + -16x + x2 = -36 + 64 Combine like terms: -36 + 64 = 28 64 + -16x + x2 = 28 Factor a perfect square on the left side: (x + -8)(x + -8) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -8) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -8 = 5.291502622 Simplifying x + -8 = 5.291502622 Reorder the terms: -8 + x = 5.291502622 Solving -8 + x = 5.291502622 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 = 5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + x = 5.291502622 + 8 x = 5.291502622 + 8 Combine like terms: 5.291502622 + 8 = 13.291502622 x = 13.291502622 Simplifying x = 13.291502622Subproblem 2
x + -8 = -5.291502622 Simplifying x + -8 = -5.291502622 Reorder the terms: -8 + x = -5.291502622 Solving -8 + x = -5.291502622 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 = -5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + x = -5.291502622 + 8 x = -5.291502622 + 8 Combine like terms: -5.291502622 + 8 = 2.708497378 x = 2.708497378 Simplifying x = 2.708497378Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.291502622, 2.708497378}Solution
x = {0, 13.291502622, 2.708497378}
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