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Simplifying 4x3 + 9x2 + -20x = 0 Reorder the terms: -20x + 9x2 + 4x3 = 0 Solving -20x + 9x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + 9x + 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 '(-20 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying -20 + 9x + 4x2 = 0 Solving -20 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + 2.25x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.25x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2.25x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.25x + x2 = 0 + 5 2.25x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.25x + x2 = 5 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 5 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 5 + 1.265625 Combine like terms: 5 + 1.265625 = 6.265625 1.265625 + 2.25x + x2 = 6.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 6.265625 Calculate the square root of the right side: 2.503123049 Break this problem into two subproblems by setting (x + 1.125) equal to 2.503123049 and -2.503123049.Subproblem 1
x + 1.125 = 2.503123049 Simplifying x + 1.125 = 2.503123049 Reorder the terms: 1.125 + x = 2.503123049 Solving 1.125 + x = 2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 2.503123049 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.503123049 + -1.125 x = 2.503123049 + -1.125 Combine like terms: 2.503123049 + -1.125 = 1.378123049 x = 1.378123049 Simplifying x = 1.378123049Subproblem 2
x + 1.125 = -2.503123049 Simplifying x + 1.125 = -2.503123049 Reorder the terms: 1.125 + x = -2.503123049 Solving 1.125 + x = -2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -2.503123049 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.503123049 + -1.125 x = -2.503123049 + -1.125 Combine like terms: -2.503123049 + -1.125 = -3.628123049 x = -3.628123049 Simplifying x = -3.628123049Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.378123049, -3.628123049}Solution
x = {0, 1.378123049, -3.628123049}
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