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Simplifying 4x2 + -29x + -12 = 0 Reorder the terms: -12 + -29x + 4x2 = 0 Solving -12 + -29x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + -7.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -7.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -7.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7.25x + x2 = 0 + 3 -7.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -7.25x + x2 = 3 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = 3 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = 3 + 13.140625 Combine like terms: 3 + 13.140625 = 16.140625 13.140625 + -7.25x + x2 = 16.140625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 16.140625 Calculate the square root of the right side: 4.01753967 Break this problem into two subproblems by setting (x + -3.625) equal to 4.01753967 and -4.01753967.Subproblem 1
x + -3.625 = 4.01753967 Simplifying x + -3.625 = 4.01753967 Reorder the terms: -3.625 + x = 4.01753967 Solving -3.625 + x = 4.01753967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 4.01753967 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 4.01753967 + 3.625 x = 4.01753967 + 3.625 Combine like terms: 4.01753967 + 3.625 = 7.64253967 x = 7.64253967 Simplifying x = 7.64253967Subproblem 2
x + -3.625 = -4.01753967 Simplifying x + -3.625 = -4.01753967 Reorder the terms: -3.625 + x = -4.01753967 Solving -3.625 + x = -4.01753967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -4.01753967 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -4.01753967 + 3.625 x = -4.01753967 + 3.625 Combine like terms: -4.01753967 + 3.625 = -0.39253967 x = -0.39253967 Simplifying x = -0.39253967Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.64253967, -0.39253967}
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