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Simplifying 6x2 + 3x + -49 = 0 Reorder the terms: -49 + 3x + 6x2 = 0 Solving -49 + 3x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -8.166666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '8.166666667' to each side of the equation. -8.166666667 + 0.5x + 8.166666667 + x2 = 0 + 8.166666667 Reorder the terms: -8.166666667 + 8.166666667 + 0.5x + x2 = 0 + 8.166666667 Combine like terms: -8.166666667 + 8.166666667 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 8.166666667 0.5x + x2 = 0 + 8.166666667 Combine like terms: 0 + 8.166666667 = 8.166666667 0.5x + x2 = 8.166666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 8.166666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 8.166666667 + 0.0625 Combine like terms: 8.166666667 + 0.0625 = 8.229166667 0.0625 + 0.5x + x2 = 8.229166667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 8.229166667 Calculate the square root of the right side: 2.868652413 Break this problem into two subproblems by setting (x + 0.25) equal to 2.868652413 and -2.868652413.Subproblem 1
x + 0.25 = 2.868652413 Simplifying x + 0.25 = 2.868652413 Reorder the terms: 0.25 + x = 2.868652413 Solving 0.25 + x = 2.868652413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.868652413 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.868652413 + -0.25 x = 2.868652413 + -0.25 Combine like terms: 2.868652413 + -0.25 = 2.618652413 x = 2.618652413 Simplifying x = 2.618652413Subproblem 2
x + 0.25 = -2.868652413 Simplifying x + 0.25 = -2.868652413 Reorder the terms: 0.25 + x = -2.868652413 Solving 0.25 + x = -2.868652413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.868652413 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.868652413 + -0.25 x = -2.868652413 + -0.25 Combine like terms: -2.868652413 + -0.25 = -3.118652413 x = -3.118652413 Simplifying x = -3.118652413Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.618652413, -3.118652413}
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