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Simplifying 185 = -16x2 + 131x + 50 Reorder the terms: 185 = 50 + 131x + -16x2 Solving 185 = 50 + 131x + -16x2 Solving for variable 'x'. Combine like terms: 185 + -50 = 135 135 + -131x + 16x2 = 50 + 131x + -16x2 + -50 + -131x + 16x2 Reorder the terms: 135 + -131x + 16x2 = 50 + -50 + 131x + -131x + -16x2 + 16x2 Combine like terms: 50 + -50 = 0 135 + -131x + 16x2 = 0 + 131x + -131x + -16x2 + 16x2 135 + -131x + 16x2 = 131x + -131x + -16x2 + 16x2 Combine like terms: 131x + -131x = 0 135 + -131x + 16x2 = 0 + -16x2 + 16x2 135 + -131x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 135 + -131x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 8.4375 + -8.1875x + x2 = 0 Move the constant term to the right: Add '-8.4375' to each side of the equation. 8.4375 + -8.1875x + -8.4375 + x2 = 0 + -8.4375 Reorder the terms: 8.4375 + -8.4375 + -8.1875x + x2 = 0 + -8.4375 Combine like terms: 8.4375 + -8.4375 = 0.0000 0.0000 + -8.1875x + x2 = 0 + -8.4375 -8.1875x + x2 = 0 + -8.4375 Combine like terms: 0 + -8.4375 = -8.4375 -8.1875x + x2 = -8.4375 The x term is -8.1875x. Take half its coefficient (-4.09375). Square it (16.75878906) and add it to both sides. Add '16.75878906' to each side of the equation. -8.1875x + 16.75878906 + x2 = -8.4375 + 16.75878906 Reorder the terms: 16.75878906 + -8.1875x + x2 = -8.4375 + 16.75878906 Combine like terms: -8.4375 + 16.75878906 = 8.32128906 16.75878906 + -8.1875x + x2 = 8.32128906 Factor a perfect square on the left side: (x + -4.09375)(x + -4.09375) = 8.32128906 Calculate the square root of the right side: 2.884664462 Break this problem into two subproblems by setting (x + -4.09375) equal to 2.884664462 and -2.884664462.Subproblem 1
x + -4.09375 = 2.884664462 Simplifying x + -4.09375 = 2.884664462 Reorder the terms: -4.09375 + x = 2.884664462 Solving -4.09375 + x = 2.884664462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.09375' to each side of the equation. -4.09375 + 4.09375 + x = 2.884664462 + 4.09375 Combine like terms: -4.09375 + 4.09375 = 0.00000 0.00000 + x = 2.884664462 + 4.09375 x = 2.884664462 + 4.09375 Combine like terms: 2.884664462 + 4.09375 = 6.978414462 x = 6.978414462 Simplifying x = 6.978414462Subproblem 2
x + -4.09375 = -2.884664462 Simplifying x + -4.09375 = -2.884664462 Reorder the terms: -4.09375 + x = -2.884664462 Solving -4.09375 + x = -2.884664462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.09375' to each side of the equation. -4.09375 + 4.09375 + x = -2.884664462 + 4.09375 Combine like terms: -4.09375 + 4.09375 = 0.00000 0.00000 + x = -2.884664462 + 4.09375 x = -2.884664462 + 4.09375 Combine like terms: -2.884664462 + 4.09375 = 1.209085538 x = 1.209085538 Simplifying x = 1.209085538Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.978414462, 1.209085538}
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