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Simplifying 2x2 + 8x3 + -23x2 + -38x = 0 Reorder the terms: -38x + 2x2 + -23x2 + 8x3 = 0 Combine like terms: 2x2 + -23x2 = -21x2 -38x + -21x2 + 8x3 = 0 Solving -38x + -21x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-38 + -21x + 8x2) = 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 '(-38 + -21x + 8x2)' equal to zero and attempt to solve: Simplifying -38 + -21x + 8x2 = 0 Solving -38 + -21x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.75 + -2.625x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -2.625x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -2.625x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -2.625x + x2 = 0 + 4.75 -2.625x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -2.625x + x2 = 4.75 The x term is -2.625x. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625x + 1.72265625 + x2 = 4.75 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = 4.75 + 1.72265625 Combine like terms: 4.75 + 1.72265625 = 6.47265625 1.72265625 + -2.625x + x2 = 6.47265625 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = 6.47265625 Calculate the square root of the right side: 2.544141555 Break this problem into two subproblems by setting (x + -1.3125) equal to 2.544141555 and -2.544141555.Subproblem 1
x + -1.3125 = 2.544141555 Simplifying x + -1.3125 = 2.544141555 Reorder the terms: -1.3125 + x = 2.544141555 Solving -1.3125 + x = 2.544141555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = 2.544141555 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = 2.544141555 + 1.3125 x = 2.544141555 + 1.3125 Combine like terms: 2.544141555 + 1.3125 = 3.856641555 x = 3.856641555 Simplifying x = 3.856641555Subproblem 2
x + -1.3125 = -2.544141555 Simplifying x + -1.3125 = -2.544141555 Reorder the terms: -1.3125 + x = -2.544141555 Solving -1.3125 + x = -2.544141555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = -2.544141555 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = -2.544141555 + 1.3125 x = -2.544141555 + 1.3125 Combine like terms: -2.544141555 + 1.3125 = -1.231641555 x = -1.231641555 Simplifying x = -1.231641555Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.856641555, -1.231641555}Solution
x = {0, 3.856641555, -1.231641555}
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