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Simplifying (3x2 + -5x + -29) + (5x2 + 8x) = 0 Reorder the terms: (-29 + -5x + 3x2) + (5x2 + 8x) = 0 Remove parenthesis around (-29 + -5x + 3x2) -29 + -5x + 3x2 + (5x2 + 8x) = 0 Reorder the terms: -29 + -5x + 3x2 + (8x + 5x2) = 0 Remove parenthesis around (8x + 5x2) -29 + -5x + 3x2 + 8x + 5x2 = 0 Reorder the terms: -29 + -5x + 8x + 3x2 + 5x2 = 0 Combine like terms: -5x + 8x = 3x -29 + 3x + 3x2 + 5x2 = 0 Combine like terms: 3x2 + 5x2 = 8x2 -29 + 3x + 8x2 = 0 Solving -29 + 3x + 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'. -3.625 + 0.375x + x2 = 0 Move the constant term to the right: Add '3.625' to each side of the equation. -3.625 + 0.375x + 3.625 + x2 = 0 + 3.625 Reorder the terms: -3.625 + 3.625 + 0.375x + x2 = 0 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + 0.375x + x2 = 0 + 3.625 0.375x + x2 = 0 + 3.625 Combine like terms: 0 + 3.625 = 3.625 0.375x + x2 = 3.625 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 3.625 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 3.625 + 0.03515625 Combine like terms: 3.625 + 0.03515625 = 3.66015625 0.03515625 + 0.375x + x2 = 3.66015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 3.66015625 Calculate the square root of the right side: 1.913153483 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.913153483 and -1.913153483.Subproblem 1
x + 0.1875 = 1.913153483 Simplifying x + 0.1875 = 1.913153483 Reorder the terms: 0.1875 + x = 1.913153483 Solving 0.1875 + x = 1.913153483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.913153483 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.913153483 + -0.1875 x = 1.913153483 + -0.1875 Combine like terms: 1.913153483 + -0.1875 = 1.725653483 x = 1.725653483 Simplifying x = 1.725653483Subproblem 2
x + 0.1875 = -1.913153483 Simplifying x + 0.1875 = -1.913153483 Reorder the terms: 0.1875 + x = -1.913153483 Solving 0.1875 + x = -1.913153483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.913153483 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.913153483 + -0.1875 x = -1.913153483 + -0.1875 Combine like terms: -1.913153483 + -0.1875 = -2.100653483 x = -2.100653483 Simplifying x = -2.100653483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.725653483, -2.100653483}
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