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Simplifying 12x2 + 37x + 7 = 0 Reorder the terms: 7 + 37x + 12x2 = 0 Solving 7 + 37x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + 3.083333333x + x2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + 3.083333333x + -0.5833333333 + x2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + 3.083333333x + x2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + 3.083333333x + x2 = 0 + -0.5833333333 3.083333333x + x2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 3.083333333x + x2 = -0.5833333333 The x term is 3.083333333x. Take half its coefficient (1.541666667). Square it (2.376736112) and add it to both sides. Add '2.376736112' to each side of the equation. 3.083333333x + 2.376736112 + x2 = -0.5833333333 + 2.376736112 Reorder the terms: 2.376736112 + 3.083333333x + x2 = -0.5833333333 + 2.376736112 Combine like terms: -0.5833333333 + 2.376736112 = 1.7934027787 2.376736112 + 3.083333333x + x2 = 1.7934027787 Factor a perfect square on the left side: (x + 1.541666667)(x + 1.541666667) = 1.7934027787 Calculate the square root of the right side: 1.33917989 Break this problem into two subproblems by setting (x + 1.541666667) equal to 1.33917989 and -1.33917989.Subproblem 1
x + 1.541666667 = 1.33917989 Simplifying x + 1.541666667 = 1.33917989 Reorder the terms: 1.541666667 + x = 1.33917989 Solving 1.541666667 + x = 1.33917989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.541666667' to each side of the equation. 1.541666667 + -1.541666667 + x = 1.33917989 + -1.541666667 Combine like terms: 1.541666667 + -1.541666667 = 0.000000000 0.000000000 + x = 1.33917989 + -1.541666667 x = 1.33917989 + -1.541666667 Combine like terms: 1.33917989 + -1.541666667 = -0.202486777 x = -0.202486777 Simplifying x = -0.202486777Subproblem 2
x + 1.541666667 = -1.33917989 Simplifying x + 1.541666667 = -1.33917989 Reorder the terms: 1.541666667 + x = -1.33917989 Solving 1.541666667 + x = -1.33917989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.541666667' to each side of the equation. 1.541666667 + -1.541666667 + x = -1.33917989 + -1.541666667 Combine like terms: 1.541666667 + -1.541666667 = 0.000000000 0.000000000 + x = -1.33917989 + -1.541666667 x = -1.33917989 + -1.541666667 Combine like terms: -1.33917989 + -1.541666667 = -2.880846557 x = -2.880846557 Simplifying x = -2.880846557Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.202486777, -2.880846557}
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