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Simplifying 12(5x2 + -32) = 3x + -7 Reorder the terms: 12(-32 + 5x2) = 3x + -7 (-32 * 12 + 5x2 * 12) = 3x + -7 (-384 + 60x2) = 3x + -7 Reorder the terms: -384 + 60x2 = -7 + 3x Solving -384 + 60x2 = -7 + 3x Solving for variable 'x'. Reorder the terms: -384 + 7 + -3x + 60x2 = -7 + 3x + 7 + -3x Combine like terms: -384 + 7 = -377 -377 + -3x + 60x2 = -7 + 3x + 7 + -3x Reorder the terms: -377 + -3x + 60x2 = -7 + 7 + 3x + -3x Combine like terms: -7 + 7 = 0 -377 + -3x + 60x2 = 0 + 3x + -3x -377 + -3x + 60x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -377 + -3x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -6.283333333 + -0.05x + x2 = 0.0 Move the constant term to the right: Add '6.283333333' to each side of the equation. -6.283333333 + -0.05x + 6.283333333 + x2 = 0.0 + 6.283333333 Reorder the terms: -6.283333333 + 6.283333333 + -0.05x + x2 = 0.0 + 6.283333333 Combine like terms: -6.283333333 + 6.283333333 = 0.000000000 0.000000000 + -0.05x + x2 = 0.0 + 6.283333333 -0.05x + x2 = 0.0 + 6.283333333 Combine like terms: 0.0 + 6.283333333 = 6.283333333 -0.05x + x2 = 6.283333333 The x term is -0.05x. Take half its coefficient (-0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. -0.05x + 0.000625 + x2 = 6.283333333 + 0.000625 Reorder the terms: 0.000625 + -0.05x + x2 = 6.283333333 + 0.000625 Combine like terms: 6.283333333 + 0.000625 = 6.283958333 0.000625 + -0.05x + x2 = 6.283958333 Factor a perfect square on the left side: (x + -0.025)(x + -0.025) = 6.283958333 Calculate the square root of the right side: 2.506782466 Break this problem into two subproblems by setting (x + -0.025) equal to 2.506782466 and -2.506782466.Subproblem 1
x + -0.025 = 2.506782466 Simplifying x + -0.025 = 2.506782466 Reorder the terms: -0.025 + x = 2.506782466 Solving -0.025 + x = 2.506782466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = 2.506782466 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 2.506782466 + 0.025 x = 2.506782466 + 0.025 Combine like terms: 2.506782466 + 0.025 = 2.531782466 x = 2.531782466 Simplifying x = 2.531782466Subproblem 2
x + -0.025 = -2.506782466 Simplifying x + -0.025 = -2.506782466 Reorder the terms: -0.025 + x = -2.506782466 Solving -0.025 + x = -2.506782466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = -2.506782466 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -2.506782466 + 0.025 x = -2.506782466 + 0.025 Combine like terms: -2.506782466 + 0.025 = -2.481782466 x = -2.481782466 Simplifying x = -2.481782466Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.531782466, -2.481782466}
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