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Simplifying 195 = -16x2 + 110x + 50 Reorder the terms: 195 = 50 + 110x + -16x2 Solving 195 = 50 + 110x + -16x2 Solving for variable 'x'. Combine like terms: 195 + -50 = 145 145 + -110x + 16x2 = 50 + 110x + -16x2 + -50 + -110x + 16x2 Reorder the terms: 145 + -110x + 16x2 = 50 + -50 + 110x + -110x + -16x2 + 16x2 Combine like terms: 50 + -50 = 0 145 + -110x + 16x2 = 0 + 110x + -110x + -16x2 + 16x2 145 + -110x + 16x2 = 110x + -110x + -16x2 + 16x2 Combine like terms: 110x + -110x = 0 145 + -110x + 16x2 = 0 + -16x2 + 16x2 145 + -110x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 145 + -110x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 9.0625 + -6.875x + x2 = 0 Move the constant term to the right: Add '-9.0625' to each side of the equation. 9.0625 + -6.875x + -9.0625 + x2 = 0 + -9.0625 Reorder the terms: 9.0625 + -9.0625 + -6.875x + x2 = 0 + -9.0625 Combine like terms: 9.0625 + -9.0625 = 0.0000 0.0000 + -6.875x + x2 = 0 + -9.0625 -6.875x + x2 = 0 + -9.0625 Combine like terms: 0 + -9.0625 = -9.0625 -6.875x + x2 = -9.0625 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 = -9.0625 + 11.81640625 Reorder the terms: 11.81640625 + -6.875x + x2 = -9.0625 + 11.81640625 Combine like terms: -9.0625 + 11.81640625 = 2.75390625 11.81640625 + -6.875x + x2 = 2.75390625 Factor a perfect square on the left side: (x + -3.4375)(x + -3.4375) = 2.75390625 Calculate the square root of the right side: 1.659489756 Break this problem into two subproblems by setting (x + -3.4375) equal to 1.659489756 and -1.659489756.Subproblem 1
x + -3.4375 = 1.659489756 Simplifying x + -3.4375 = 1.659489756 Reorder the terms: -3.4375 + x = 1.659489756 Solving -3.4375 + x = 1.659489756 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 = 1.659489756 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = 1.659489756 + 3.4375 x = 1.659489756 + 3.4375 Combine like terms: 1.659489756 + 3.4375 = 5.096989756 x = 5.096989756 Simplifying x = 5.096989756Subproblem 2
x + -3.4375 = -1.659489756 Simplifying x + -3.4375 = -1.659489756 Reorder the terms: -3.4375 + x = -1.659489756 Solving -3.4375 + x = -1.659489756 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 = -1.659489756 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + x = -1.659489756 + 3.4375 x = -1.659489756 + 3.4375 Combine like terms: -1.659489756 + 3.4375 = 1.778010244 x = 1.778010244 Simplifying x = 1.778010244Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.096989756, 1.778010244}
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