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Simplifying 187 = -16x2 + 110x Reorder the terms: 187 = 110x + -16x2 Solving 187 = 110x + -16x2 Solving for variable 'x'. Reorder the terms: 187 + -110x + 16x2 = 110x + -110x + -16x2 + 16x2 Combine like terms: 110x + -110x = 0 187 + -110x + 16x2 = 0 + -16x2 + 16x2 187 + -110x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 187 + -110x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 11.6875 + -6.875x + x2 = 0 Move the constant term to the right: Add '-11.6875' to each side of the equation. 11.6875 + -6.875x + -11.6875 + x2 = 0 + -11.6875 Reorder the terms: 11.6875 + -11.6875 + -6.875x + x2 = 0 + -11.6875 Combine like terms: 11.6875 + -11.6875 = 0.0000 0.0000 + -6.875x + x2 = 0 + -11.6875 -6.875x + x2 = 0 + -11.6875 Combine like terms: 0 + -11.6875 = -11.6875 -6.875x + x2 = -11.6875 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 = -11.6875 + 11.81640625 Reorder the terms: 11.81640625 + -6.875x + x2 = -11.6875 + 11.81640625 Combine like terms: -11.6875 + 11.81640625 = 0.12890625 11.81640625 + -6.875x + x2 = 0.12890625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (x + -3.4375) equal to 0.359035165 and -0.359035165.Subproblem 1
x + -3.4375 = 0.359035165 Simplifying x + -3.4375 = 0.359035165 Reorder the terms: -3.4375 + x = 0.359035165 Solving -3.4375 + x = 0.359035165 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 = 0.359035165 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 0.359035165 + 3.4375 x = 0.359035165 + 3.4375 Combine like terms: 0.359035165 + 3.4375 = 3.796535165 x = 3.796535165 Simplifying x = 3.796535165Subproblem 2
x + -3.4375 = -0.359035165 Simplifying x + -3.4375 = -0.359035165 Reorder the terms: -3.4375 + x = -0.359035165 Solving -3.4375 + x = -0.359035165 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 = -0.359035165 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -0.359035165 + 3.4375 x = -0.359035165 + 3.4375 Combine like terms: -0.359035165 + 3.4375 = 3.078464835 x = 3.078464835 Simplifying x = 3.078464835Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.796535165, 3.078464835}
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