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Simplifying 4x3 + -17x2 + 5x = 0 Reorder the terms: 5x + -17x2 + 4x3 = 0 Solving 5x + -17x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + -17x + 4x2) = 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 '(5 + -17x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + -17x + 4x2 = 0 Solving 5 + -17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -4.25x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -4.25x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -4.25x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -4.25x + x2 = 0 + -1.25 -4.25x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -4.25x + x2 = -1.25 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -1.25 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -1.25 + 4.515625 Combine like terms: -1.25 + 4.515625 = 3.265625 4.515625 + -4.25x + x2 = 3.265625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + -2.125) equal to 1.807104037 and -1.807104037.Subproblem 1
x + -2.125 = 1.807104037 Simplifying x + -2.125 = 1.807104037 Reorder the terms: -2.125 + x = 1.807104037 Solving -2.125 + x = 1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 1.807104037 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.807104037 + 2.125 x = 1.807104037 + 2.125 Combine like terms: 1.807104037 + 2.125 = 3.932104037 x = 3.932104037 Simplifying x = 3.932104037Subproblem 2
x + -2.125 = -1.807104037 Simplifying x + -2.125 = -1.807104037 Reorder the terms: -2.125 + x = -1.807104037 Solving -2.125 + x = -1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -1.807104037 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.807104037 + 2.125 x = -1.807104037 + 2.125 Combine like terms: -1.807104037 + 2.125 = 0.317895963 x = 0.317895963 Simplifying x = 0.317895963Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.932104037, 0.317895963}Solution
x = {0, 3.932104037, 0.317895963}
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