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Simplifying 3x2 + 12x + -34 = 0 Reorder the terms: -34 + 12x + 3x2 = 0 Solving -34 + 12x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.33333333 + 4x + x2 = 0 Move the constant term to the right: Add '11.33333333' to each side of the equation. -11.33333333 + 4x + 11.33333333 + x2 = 0 + 11.33333333 Reorder the terms: -11.33333333 + 11.33333333 + 4x + x2 = 0 + 11.33333333 Combine like terms: -11.33333333 + 11.33333333 = 0.00000000 0.00000000 + 4x + x2 = 0 + 11.33333333 4x + x2 = 0 + 11.33333333 Combine like terms: 0 + 11.33333333 = 11.33333333 4x + x2 = 11.33333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 11.33333333 + 4 Reorder the terms: 4 + 4x + x2 = 11.33333333 + 4 Combine like terms: 11.33333333 + 4 = 15.33333333 4 + 4x + x2 = 15.33333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 15.33333333 Calculate the square root of the right side: 3.915780041 Break this problem into two subproblems by setting (x + 2) equal to 3.915780041 and -3.915780041.Subproblem 1
x + 2 = 3.915780041 Simplifying x + 2 = 3.915780041 Reorder the terms: 2 + x = 3.915780041 Solving 2 + x = 3.915780041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.915780041 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.915780041 + -2 x = 3.915780041 + -2 Combine like terms: 3.915780041 + -2 = 1.915780041 x = 1.915780041 Simplifying x = 1.915780041Subproblem 2
x + 2 = -3.915780041 Simplifying x + 2 = -3.915780041 Reorder the terms: 2 + x = -3.915780041 Solving 2 + x = -3.915780041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.915780041 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.915780041 + -2 x = -3.915780041 + -2 Combine like terms: -3.915780041 + -2 = -5.915780041 x = -5.915780041 Simplifying x = -5.915780041Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.915780041, -5.915780041}
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