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Simplifying 3x2 + 12x + -35 = 0 Reorder the terms: -35 + 12x + 3x2 = 0 Solving -35 + 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'. -11.66666667 + 4x + x2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + 4x + 11.66666667 + x2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + 4x + x2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + 4x + x2 = 0 + 11.66666667 4x + x2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 4x + x2 = 11.66666667 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 = 11.66666667 + 4 Reorder the terms: 4 + 4x + x2 = 11.66666667 + 4 Combine like terms: 11.66666667 + 4 = 15.66666667 4 + 4x + x2 = 15.66666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 15.66666667 Calculate the square root of the right side: 3.958114029 Break this problem into two subproblems by setting (x + 2) equal to 3.958114029 and -3.958114029.Subproblem 1
x + 2 = 3.958114029 Simplifying x + 2 = 3.958114029 Reorder the terms: 2 + x = 3.958114029 Solving 2 + x = 3.958114029 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 = 3.958114029 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.958114029 + -2 x = 3.958114029 + -2 Combine like terms: 3.958114029 + -2 = 1.958114029 x = 1.958114029 Simplifying x = 1.958114029Subproblem 2
x + 2 = -3.958114029 Simplifying x + 2 = -3.958114029 Reorder the terms: 2 + x = -3.958114029 Solving 2 + x = -3.958114029 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 = -3.958114029 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.958114029 + -2 x = -3.958114029 + -2 Combine like terms: -3.958114029 + -2 = -5.958114029 x = -5.958114029 Simplifying x = -5.958114029Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.958114029, -5.958114029}
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