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Simplifying -16x2 + 110x + 5 = 0 Reorder the terms: 5 + 110x + -16x2 = 0 Solving 5 + 110x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -6.875x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -6.875x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -6.875x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -6.875x + x2 = 0 + 0.3125 -6.875x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -6.875x + x2 = 0.3125 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 = 0.3125 + 11.81640625 Reorder the terms: 11.81640625 + -6.875x + x2 = 0.3125 + 11.81640625 Combine like terms: 0.3125 + 11.81640625 = 12.12890625 11.81640625 + -6.875x + x2 = 12.12890625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 12.12890625 Calculate the square root of the right side: 3.482657929 Break this problem into two subproblems by setting (x + -3.4375) equal to 3.482657929 and -3.482657929.Subproblem 1
x + -3.4375 = 3.482657929 Simplifying x + -3.4375 = 3.482657929 Reorder the terms: -3.4375 + x = 3.482657929 Solving -3.4375 + x = 3.482657929 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 = 3.482657929 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 3.482657929 + 3.4375 x = 3.482657929 + 3.4375 Combine like terms: 3.482657929 + 3.4375 = 6.920157929 x = 6.920157929 Simplifying x = 6.920157929Subproblem 2
x + -3.4375 = -3.482657929 Simplifying x + -3.4375 = -3.482657929 Reorder the terms: -3.4375 + x = -3.482657929 Solving -3.4375 + x = -3.482657929 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 = -3.482657929 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -3.482657929 + 3.4375 x = -3.482657929 + 3.4375 Combine like terms: -3.482657929 + 3.4375 = -0.045157929 x = -0.045157929 Simplifying x = -0.045157929Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.920157929, -0.045157929}
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