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Simplifying 3x2 + 5x2 + -21x + -35 = 0 Reorder the terms: -35 + -21x + 3x2 + 5x2 = 0 Combine like terms: 3x2 + 5x2 = 8x2 -35 + -21x + 8x2 = 0 Solving -35 + -21x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + -2.625x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + -2.625x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + -2.625x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + -2.625x + x2 = 0 + 4.375 -2.625x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 -2.625x + x2 = 4.375 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 = 4.375 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = 4.375 + 1.72265625 Combine like terms: 4.375 + 1.72265625 = 6.09765625 1.72265625 + -2.625x + x2 = 6.09765625 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = 6.09765625 Calculate the square root of the right side: 2.469343283 Break this problem into two subproblems by setting (x + -1.3125) equal to 2.469343283 and -2.469343283.Subproblem 1
x + -1.3125 = 2.469343283 Simplifying x + -1.3125 = 2.469343283 Reorder the terms: -1.3125 + x = 2.469343283 Solving -1.3125 + x = 2.469343283 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 = 2.469343283 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = 2.469343283 + 1.3125 x = 2.469343283 + 1.3125 Combine like terms: 2.469343283 + 1.3125 = 3.781843283 x = 3.781843283 Simplifying x = 3.781843283Subproblem 2
x + -1.3125 = -2.469343283 Simplifying x + -1.3125 = -2.469343283 Reorder the terms: -1.3125 + x = -2.469343283 Solving -1.3125 + x = -2.469343283 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 = -2.469343283 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = -2.469343283 + 1.3125 x = -2.469343283 + 1.3125 Combine like terms: -2.469343283 + 1.3125 = -1.156843283 x = -1.156843283 Simplifying x = -1.156843283Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.781843283, -1.156843283}
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