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Simplifying 50 = -0.3476x2 + 10.948x + -23.078 Reorder the terms: 50 = -23.078 + 10.948x + -0.3476x2 Solving 50 = -23.078 + 10.948x + -0.3476x2 Solving for variable 'x'. Combine like terms: 50 + 23.078 = 73.078 73.078 + -10.948x + 0.3476x2 = -23.078 + 10.948x + -0.3476x2 + 23.078 + -10.948x + 0.3476x2 Reorder the terms: 73.078 + -10.948x + 0.3476x2 = -23.078 + 23.078 + 10.948x + -10.948x + -0.3476x2 + 0.3476x2 Combine like terms: -23.078 + 23.078 = 0.000 73.078 + -10.948x + 0.3476x2 = 0.000 + 10.948x + -10.948x + -0.3476x2 + 0.3476x2 73.078 + -10.948x + 0.3476x2 = 10.948x + -10.948x + -0.3476x2 + 0.3476x2 Combine like terms: 10.948x + -10.948x = 0.000 73.078 + -10.948x + 0.3476x2 = 0.000 + -0.3476x2 + 0.3476x2 73.078 + -10.948x + 0.3476x2 = -0.3476x2 + 0.3476x2 Combine like terms: -0.3476x2 + 0.3476x2 = 0.0000 73.078 + -10.948x + 0.3476x2 = 0.0000 Begin completing the square. Divide all terms by 0.3476 the coefficient of the squared term: Divide each side by '0.3476'. 210.2359033 + -31.49597238x + x2 = 0 Move the constant term to the right: Add '-210.2359033' to each side of the equation. 210.2359033 + -31.49597238x + -210.2359033 + x2 = 0 + -210.2359033 Reorder the terms: 210.2359033 + -210.2359033 + -31.49597238x + x2 = 0 + -210.2359033 Combine like terms: 210.2359033 + -210.2359033 = 0.0000000 0.0000000 + -31.49597238x + x2 = 0 + -210.2359033 -31.49597238x + x2 = 0 + -210.2359033 Combine like terms: 0 + -210.2359033 = -210.2359033 -31.49597238x + x2 = -210.2359033 The x term is -31.49597238x. Take half its coefficient (-15.74798619). Square it (247.9990690) and add it to both sides. Add '247.9990690' to each side of the equation. -31.49597238x + 247.9990690 + x2 = -210.2359033 + 247.9990690 Reorder the terms: 247.9990690 + -31.49597238x + x2 = -210.2359033 + 247.9990690 Combine like terms: -210.2359033 + 247.9990690 = 37.7631657 247.9990690 + -31.49597238x + x2 = 37.7631657 Factor a perfect square on the left side: (x + -15.74798619)(x + -15.74798619) = 37.7631657 Calculate the square root of the right side: 6.14517418 Break this problem into two subproblems by setting (x + -15.74798619) equal to 6.14517418 and -6.14517418.Subproblem 1
x + -15.74798619 = 6.14517418 Simplifying x + -15.74798619 = 6.14517418 Reorder the terms: -15.74798619 + x = 6.14517418 Solving -15.74798619 + x = 6.14517418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.74798619' to each side of the equation. -15.74798619 + 15.74798619 + x = 6.14517418 + 15.74798619 Combine like terms: -15.74798619 + 15.74798619 = 0.00000000 0.00000000 + x = 6.14517418 + 15.74798619 x = 6.14517418 + 15.74798619 Combine like terms: 6.14517418 + 15.74798619 = 21.89316037 x = 21.89316037 Simplifying x = 21.89316037Subproblem 2
x + -15.74798619 = -6.14517418 Simplifying x + -15.74798619 = -6.14517418 Reorder the terms: -15.74798619 + x = -6.14517418 Solving -15.74798619 + x = -6.14517418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.74798619' to each side of the equation. -15.74798619 + 15.74798619 + x = -6.14517418 + 15.74798619 Combine like terms: -15.74798619 + 15.74798619 = 0.00000000 0.00000000 + x = -6.14517418 + 15.74798619 x = -6.14517418 + 15.74798619 Combine like terms: -6.14517418 + 15.74798619 = 9.60281201 x = 9.60281201 Simplifying x = 9.60281201Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.89316037, 9.60281201}
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