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Simplifying 6x2 + 49x + -381 = 0 Reorder the terms: -381 + 49x + 6x2 = 0 Solving -381 + 49x + 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'. -63.5 + 8.166666667x + x2 = 0 Move the constant term to the right: Add '63.5' to each side of the equation. -63.5 + 8.166666667x + 63.5 + x2 = 0 + 63.5 Reorder the terms: -63.5 + 63.5 + 8.166666667x + x2 = 0 + 63.5 Combine like terms: -63.5 + 63.5 = 0.0 0.0 + 8.166666667x + x2 = 0 + 63.5 8.166666667x + x2 = 0 + 63.5 Combine like terms: 0 + 63.5 = 63.5 8.166666667x + x2 = 63.5 The x term is 8.166666667x. Take half its coefficient (4.083333334). Square it (16.67361112) and add it to both sides. Add '16.67361112' to each side of the equation. 8.166666667x + 16.67361112 + x2 = 63.5 + 16.67361112 Reorder the terms: 16.67361112 + 8.166666667x + x2 = 63.5 + 16.67361112 Combine like terms: 63.5 + 16.67361112 = 80.17361112 16.67361112 + 8.166666667x + x2 = 80.17361112 Factor a perfect square on the left side: (x + 4.083333334)(x + 4.083333334) = 80.17361112 Calculate the square root of the right side: 8.953971807 Break this problem into two subproblems by setting (x + 4.083333334) equal to 8.953971807 and -8.953971807.Subproblem 1
x + 4.083333334 = 8.953971807 Simplifying x + 4.083333334 = 8.953971807 Reorder the terms: 4.083333334 + x = 8.953971807 Solving 4.083333334 + x = 8.953971807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.083333334' to each side of the equation. 4.083333334 + -4.083333334 + x = 8.953971807 + -4.083333334 Combine like terms: 4.083333334 + -4.083333334 = 0.000000000 0.000000000 + x = 8.953971807 + -4.083333334 x = 8.953971807 + -4.083333334 Combine like terms: 8.953971807 + -4.083333334 = 4.870638473 x = 4.870638473 Simplifying x = 4.870638473Subproblem 2
x + 4.083333334 = -8.953971807 Simplifying x + 4.083333334 = -8.953971807 Reorder the terms: 4.083333334 + x = -8.953971807 Solving 4.083333334 + x = -8.953971807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.083333334' to each side of the equation. 4.083333334 + -4.083333334 + x = -8.953971807 + -4.083333334 Combine like terms: 4.083333334 + -4.083333334 = 0.000000000 0.000000000 + x = -8.953971807 + -4.083333334 x = -8.953971807 + -4.083333334 Combine like terms: -8.953971807 + -4.083333334 = -13.037305141 x = -13.037305141 Simplifying x = -13.037305141Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.870638473, -13.037305141}
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