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Simplifying 2x5 + -17x3 + 34x = 0 Reorder the terms: 34x + -17x3 + 2x5 = 0 Solving 34x + -17x3 + 2x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(34 + -17x2 + 2x4) = 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 '(34 + -17x2 + 2x4)' equal to zero and attempt to solve: Simplifying 34 + -17x2 + 2x4 = 0 Solving 34 + -17x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 17 + -8.5x2 + x4 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -8.5x2 + -17 + x4 = 0 + -17 Reorder the terms: 17 + -17 + -8.5x2 + x4 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -8.5x2 + x4 = 0 + -17 -8.5x2 + x4 = 0 + -17 Combine like terms: 0 + -17 = -17 -8.5x2 + x4 = -17 The x term is -8.5x2. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x2 + 18.0625 + x4 = -17 + 18.0625 Reorder the terms: 18.0625 + -8.5x2 + x4 = -17 + 18.0625 Combine like terms: -17 + 18.0625 = 1.0625 18.0625 + -8.5x2 + x4 = 1.0625 Factor a perfect square on the left side: (x2 + -4.25)(x2 + -4.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x2 + -4.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x2 + -4.25 = 1.030776406 Simplifying x2 + -4.25 = 1.030776406 Reorder the terms: -4.25 + x2 = 1.030776406 Solving -4.25 + x2 = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x2 = 1.030776406 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x2 = 1.030776406 + 4.25 x2 = 1.030776406 + 4.25 Combine like terms: 1.030776406 + 4.25 = 5.280776406 x2 = 5.280776406 Simplifying x2 = 5.280776406 Take the square root of each side: x = {-2.297993996, 2.297993996}Subproblem 2
x2 + -4.25 = -1.030776406 Simplifying x2 + -4.25 = -1.030776406 Reorder the terms: -4.25 + x2 = -1.030776406 Solving -4.25 + x2 = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x2 = -1.030776406 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x2 = -1.030776406 + 4.25 x2 = -1.030776406 + 4.25 Combine like terms: -1.030776406 + 4.25 = 3.219223594 x2 = 3.219223594 Simplifying x2 = 3.219223594 Take the square root of each side: x = {-1.794219494, 1.794219494}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.297993996, 2.297993996, -1.794219494, 1.794219494}Solution
x = {0, -2.297993996, 2.297993996, -1.794219494, 1.794219494}
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