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Simplifying -16x2 + 110x = 185 Reorder the terms: 110x + -16x2 = 185 Solving 110x + -16x2 = 185 Solving for variable 'x'. Reorder the terms: -185 + 110x + -16x2 = 185 + -185 Combine like terms: 185 + -185 = 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 = 0.25390625 11.81640625 + -6.875x + x2 = 0.25390625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (x + -3.4375) equal to 0.503891109 and -0.503891109.Subproblem 1
x + -3.4375 = 0.503891109 Simplifying x + -3.4375 = 0.503891109 Reorder the terms: -3.4375 + x = 0.503891109 Solving -3.4375 + x = 0.503891109 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 = 0.503891109 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 0.503891109 + 3.4375 x = 0.503891109 + 3.4375 Combine like terms: 0.503891109 + 3.4375 = 3.941391109 x = 3.941391109 Simplifying x = 3.941391109Subproblem 2
x + -3.4375 = -0.503891109 Simplifying x + -3.4375 = -0.503891109 Reorder the terms: -3.4375 + x = -0.503891109 Solving -3.4375 + x = -0.503891109 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 = -0.503891109 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -0.503891109 + 3.4375 x = -0.503891109 + 3.4375 Combine like terms: -0.503891109 + 3.4375 = 2.933608891 x = 2.933608891 Simplifying x = 2.933608891Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.941391109, 2.933608891}
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