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Simplifying 20x4 + -41x3 = 20x2 Reorder the terms: -41x3 + 20x4 = 20x2 Solving -41x3 + 20x4 = 20x2 Solving for variable 'x'. Reorder the terms: -20x2 + -41x3 + 20x4 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -20x2 + -41x3 + 20x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-20 + -41x + 20x2) = 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 '(-20 + -41x + 20x2)' equal to zero and attempt to solve: Simplifying -20 + -41x + 20x2 = 0 Solving -20 + -41x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1 + -2.05x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.05x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.05x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.05x + x2 = 0 + 1 -2.05x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.05x + x2 = 1 The x term is -2.05x. Take half its coefficient (-1.025). Square it (1.050625) and add it to both sides. Add '1.050625' to each side of the equation. -2.05x + 1.050625 + x2 = 1 + 1.050625 Reorder the terms: 1.050625 + -2.05x + x2 = 1 + 1.050625 Combine like terms: 1 + 1.050625 = 2.050625 1.050625 + -2.05x + x2 = 2.050625 Factor a perfect square on the left side: (x + -1.025)(x + -1.025) = 2.050625 Calculate the square root of the right side: 1.432000349 Break this problem into two subproblems by setting (x + -1.025) equal to 1.432000349 and -1.432000349.Subproblem 1
x + -1.025 = 1.432000349 Simplifying x + -1.025 = 1.432000349 Reorder the terms: -1.025 + x = 1.432000349 Solving -1.025 + x = 1.432000349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.025' to each side of the equation. -1.025 + 1.025 + x = 1.432000349 + 1.025 Combine like terms: -1.025 + 1.025 = 0.000 0.000 + x = 1.432000349 + 1.025 x = 1.432000349 + 1.025 Combine like terms: 1.432000349 + 1.025 = 2.457000349 x = 2.457000349 Simplifying x = 2.457000349Subproblem 2
x + -1.025 = -1.432000349 Simplifying x + -1.025 = -1.432000349 Reorder the terms: -1.025 + x = -1.432000349 Solving -1.025 + x = -1.432000349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.025' to each side of the equation. -1.025 + 1.025 + x = -1.432000349 + 1.025 Combine like terms: -1.025 + 1.025 = 0.000 0.000 + x = -1.432000349 + 1.025 x = -1.432000349 + 1.025 Combine like terms: -1.432000349 + 1.025 = -0.407000349 x = -0.407000349 Simplifying x = -0.407000349Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.457000349, -0.407000349}Solution
x = {0, 2.457000349, -0.407000349}
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