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Simplifying 8x2 = 30 + 433x Solving 8x2 = 30 + 433x Solving for variable 'x'. Reorder the terms: -30 + -433x + 8x2 = 30 + 433x + -30 + -433x Reorder the terms: -30 + -433x + 8x2 = 30 + -30 + 433x + -433x Combine like terms: 30 + -30 = 0 -30 + -433x + 8x2 = 0 + 433x + -433x -30 + -433x + 8x2 = 433x + -433x Combine like terms: 433x + -433x = 0 -30 + -433x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.75 + -54.125x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -54.125x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -54.125x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -54.125x + x2 = 0 + 3.75 -54.125x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -54.125x + x2 = 3.75 The x term is -54.125x. Take half its coefficient (-27.0625). Square it (732.3789063) and add it to both sides. Add '732.3789063' to each side of the equation. -54.125x + 732.3789063 + x2 = 3.75 + 732.3789063 Reorder the terms: 732.3789063 + -54.125x + x2 = 3.75 + 732.3789063 Combine like terms: 3.75 + 732.3789063 = 736.1289063 732.3789063 + -54.125x + x2 = 736.1289063 Factor a perfect square on the left side: (x + -27.0625)(x + -27.0625) = 736.1289063 Calculate the square root of the right side: 27.131695603 Break this problem into two subproblems by setting (x + -27.0625) equal to 27.131695603 and -27.131695603.Subproblem 1
x + -27.0625 = 27.131695603 Simplifying x + -27.0625 = 27.131695603 Reorder the terms: -27.0625 + x = 27.131695603 Solving -27.0625 + x = 27.131695603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.0625' to each side of the equation. -27.0625 + 27.0625 + x = 27.131695603 + 27.0625 Combine like terms: -27.0625 + 27.0625 = 0.0000 0.0000 + x = 27.131695603 + 27.0625 x = 27.131695603 + 27.0625 Combine like terms: 27.131695603 + 27.0625 = 54.194195603 x = 54.194195603 Simplifying x = 54.194195603Subproblem 2
x + -27.0625 = -27.131695603 Simplifying x + -27.0625 = -27.131695603 Reorder the terms: -27.0625 + x = -27.131695603 Solving -27.0625 + x = -27.131695603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.0625' to each side of the equation. -27.0625 + 27.0625 + x = -27.131695603 + 27.0625 Combine like terms: -27.0625 + 27.0625 = 0.0000 0.0000 + x = -27.131695603 + 27.0625 x = -27.131695603 + 27.0625 Combine like terms: -27.131695603 + 27.0625 = -0.069195603 x = -0.069195603 Simplifying x = -0.069195603Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.194195603, -0.069195603}
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