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Simplifying 12x2 + 7x + -381 = 0 Reorder the terms: -381 + 7x + 12x2 = 0 Solving -381 + 7x + 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'. -31.75 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '31.75' to each side of the equation. -31.75 + 0.5833333333x + 31.75 + x2 = 0 + 31.75 Reorder the terms: -31.75 + 31.75 + 0.5833333333x + x2 = 0 + 31.75 Combine like terms: -31.75 + 31.75 = 0.00 0.00 + 0.5833333333x + x2 = 0 + 31.75 0.5833333333x + x2 = 0 + 31.75 Combine like terms: 0 + 31.75 = 31.75 0.5833333333x + x2 = 31.75 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = 31.75 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = 31.75 + 0.08506944446 Combine like terms: 31.75 + 0.08506944446 = 31.83506944446 0.08506944446 + 0.5833333333x + x2 = 31.83506944446 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = 31.83506944446 Calculate the square root of the right side: 5.642257478 Break this problem into two subproblems by setting (x + 0.2916666667) equal to 5.642257478 and -5.642257478.Subproblem 1
x + 0.2916666667 = 5.642257478 Simplifying x + 0.2916666667 = 5.642257478 Reorder the terms: 0.2916666667 + x = 5.642257478 Solving 0.2916666667 + x = 5.642257478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = 5.642257478 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = 5.642257478 + -0.2916666667 x = 5.642257478 + -0.2916666667 Combine like terms: 5.642257478 + -0.2916666667 = 5.3505908113 x = 5.3505908113 Simplifying x = 5.3505908113Subproblem 2
x + 0.2916666667 = -5.642257478 Simplifying x + 0.2916666667 = -5.642257478 Reorder the terms: 0.2916666667 + x = -5.642257478 Solving 0.2916666667 + x = -5.642257478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = -5.642257478 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = -5.642257478 + -0.2916666667 x = -5.642257478 + -0.2916666667 Combine like terms: -5.642257478 + -0.2916666667 = -5.9339241447 x = -5.9339241447 Simplifying x = -5.9339241447Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.3505908113, -5.9339241447}
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