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Simplifying 6x2 + -49x + -30 = 0 Reorder the terms: -30 + -49x + 6x2 = 0 Solving -30 + -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'. -5 + -8.166666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -8.166666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -8.166666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8.166666667x + x2 = 0 + 5 -8.166666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8.166666667x + x2 = 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 = 5 + 16.67361112 Reorder the terms: 16.67361112 + -8.166666667x + x2 = 5 + 16.67361112 Combine like terms: 5 + 16.67361112 = 21.67361112 16.67361112 + -8.166666667x + x2 = 21.67361112 Factor a perfect square on the left side: (x + -4.083333334)(x + -4.083333334) = 21.67361112 Calculate the square root of the right side: 4.655492575 Break this problem into two subproblems by setting (x + -4.083333334) equal to 4.655492575 and -4.655492575.Subproblem 1
x + -4.083333334 = 4.655492575 Simplifying x + -4.083333334 = 4.655492575 Reorder the terms: -4.083333334 + x = 4.655492575 Solving -4.083333334 + x = 4.655492575 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 = 4.655492575 + 4.083333334 Combine like terms: -4.083333334 + 4.083333334 = 0.000000000 0.000000000 + x = 4.655492575 + 4.083333334 x = 4.655492575 + 4.083333334 Combine like terms: 4.655492575 + 4.083333334 = 8.738825909 x = 8.738825909 Simplifying x = 8.738825909Subproblem 2
x + -4.083333334 = -4.655492575 Simplifying x + -4.083333334 = -4.655492575 Reorder the terms: -4.083333334 + x = -4.655492575 Solving -4.083333334 + x = -4.655492575 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 = -4.655492575 + 4.083333334 Combine like terms: -4.083333334 + 4.083333334 = 0.000000000 0.000000000 + x = -4.655492575 + 4.083333334 x = -4.655492575 + 4.083333334 Combine like terms: -4.655492575 + 4.083333334 = -0.572159241 x = -0.572159241 Simplifying x = -0.572159241Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.738825909, -0.572159241}
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