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Simplifying 49 + -98x + 12x2 = 0 Solving 49 + -98x + 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'. 4.083333333 + -8.166666667x + x2 = 0 Move the constant term to the right: Add '-4.083333333' to each side of the equation. 4.083333333 + -8.166666667x + -4.083333333 + x2 = 0 + -4.083333333 Reorder the terms: 4.083333333 + -4.083333333 + -8.166666667x + x2 = 0 + -4.083333333 Combine like terms: 4.083333333 + -4.083333333 = 0.000000000 0.000000000 + -8.166666667x + x2 = 0 + -4.083333333 -8.166666667x + x2 = 0 + -4.083333333 Combine like terms: 0 + -4.083333333 = -4.083333333 -8.166666667x + x2 = -4.083333333 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 = -4.083333333 + 16.67361112 Reorder the terms: 16.67361112 + -8.166666667x + x2 = -4.083333333 + 16.67361112 Combine like terms: -4.083333333 + 16.67361112 = 12.590277787 16.67361112 + -8.166666667x + x2 = 12.590277787 Factor a perfect square on the left side: (x + -4.083333334)(x + -4.083333334) = 12.590277787 Calculate the square root of the right side: 3.548278144 Break this problem into two subproblems by setting (x + -4.083333334) equal to 3.548278144 and -3.548278144.Subproblem 1
x + -4.083333334 = 3.548278144 Simplifying x + -4.083333334 = 3.548278144 Reorder the terms: -4.083333334 + x = 3.548278144 Solving -4.083333334 + x = 3.548278144 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 = 3.548278144 + 4.083333334 Combine like terms: -4.083333334 + 4.083333334 = 0.000000000 0.000000000 + x = 3.548278144 + 4.083333334 x = 3.548278144 + 4.083333334 Combine like terms: 3.548278144 + 4.083333334 = 7.631611478 x = 7.631611478 Simplifying x = 7.631611478Subproblem 2
x + -4.083333334 = -3.548278144 Simplifying x + -4.083333334 = -3.548278144 Reorder the terms: -4.083333334 + x = -3.548278144 Solving -4.083333334 + x = -3.548278144 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 = -3.548278144 + 4.083333334 Combine like terms: -4.083333334 + 4.083333334 = 0.000000000 0.000000000 + x = -3.548278144 + 4.083333334 x = -3.548278144 + 4.083333334 Combine like terms: -3.548278144 + 4.083333334 = 0.53505519 x = 0.53505519 Simplifying x = 0.53505519Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.631611478, 0.53505519}
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