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Simplifying 185 = 16x2 + 110x Reorder the terms: 185 = 110x + 16x2 Solving 185 = 110x + 16x2 Solving for variable 'x'. Reorder the terms: 185 + -110x + -16x2 = 110x + -110x + 16x2 + -16x2 Combine like terms: 110x + -110x = 0 185 + -110x + -16x2 = 0 + 16x2 + -16x2 185 + -110x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 185 + -110x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -11.5625 + 6.875x + x2 = 0 Move the constant term to the right: Add '11.5625' to each side of the equation. -11.5625 + 6.875x + 11.5625 + x2 = 0 + 11.5625 Reorder the terms: -11.5625 + 11.5625 + 6.875x + x2 = 0 + 11.5625 Combine like terms: -11.5625 + 11.5625 = 0.0000 0.0000 + 6.875x + x2 = 0 + 11.5625 6.875x + x2 = 0 + 11.5625 Combine like terms: 0 + 11.5625 = 11.5625 6.875x + x2 = 11.5625 The x term is 6.875x. Take half its coefficient (3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. 6.875x + 11.81640625 + x2 = 11.5625 + 11.81640625 Reorder the terms: 11.81640625 + 6.875x + x2 = 11.5625 + 11.81640625 Combine like terms: 11.5625 + 11.81640625 = 23.37890625 11.81640625 + 6.875x + x2 = 23.37890625 Factor a perfect square on the left side: (x + 3.4375)(x + 3.4375) = 23.37890625 Calculate the square root of the right side: 4.835173859 Break this problem into two subproblems by setting (x + 3.4375) equal to 4.835173859 and -4.835173859.Subproblem 1
x + 3.4375 = 4.835173859 Simplifying x + 3.4375 = 4.835173859 Reorder the terms: 3.4375 + x = 4.835173859 Solving 3.4375 + x = 4.835173859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + x = 4.835173859 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + x = 4.835173859 + -3.4375 x = 4.835173859 + -3.4375 Combine like terms: 4.835173859 + -3.4375 = 1.397673859 x = 1.397673859 Simplifying x = 1.397673859Subproblem 2
x + 3.4375 = -4.835173859 Simplifying x + 3.4375 = -4.835173859 Reorder the terms: 3.4375 + x = -4.835173859 Solving 3.4375 + x = -4.835173859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + x = -4.835173859 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + x = -4.835173859 + -3.4375 x = -4.835173859 + -3.4375 Combine like terms: -4.835173859 + -3.4375 = -8.272673859 x = -8.272673859 Simplifying x = -8.272673859Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.397673859, -8.272673859}
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