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Simplifying 0 = -16x2 + 90x + -95 Reorder the terms: 0 = -95 + 90x + -16x2 Solving 0 = -95 + 90x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 95 = 95 95 + -90x + 16x2 = -95 + 90x + -16x2 + 95 + -90x + 16x2 Reorder the terms: 95 + -90x + 16x2 = -95 + 95 + 90x + -90x + -16x2 + 16x2 Combine like terms: -95 + 95 = 0 95 + -90x + 16x2 = 0 + 90x + -90x + -16x2 + 16x2 95 + -90x + 16x2 = 90x + -90x + -16x2 + 16x2 Combine like terms: 90x + -90x = 0 95 + -90x + 16x2 = 0 + -16x2 + 16x2 95 + -90x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 95 + -90x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.9375 + -5.625x + x2 = 0 Move the constant term to the right: Add '-5.9375' to each side of the equation. 5.9375 + -5.625x + -5.9375 + x2 = 0 + -5.9375 Reorder the terms: 5.9375 + -5.9375 + -5.625x + x2 = 0 + -5.9375 Combine like terms: 5.9375 + -5.9375 = 0.0000 0.0000 + -5.625x + x2 = 0 + -5.9375 -5.625x + x2 = 0 + -5.9375 Combine like terms: 0 + -5.9375 = -5.9375 -5.625x + x2 = -5.9375 The x term is -5.625x. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625x + 7.91015625 + x2 = -5.9375 + 7.91015625 Reorder the terms: 7.91015625 + -5.625x + x2 = -5.9375 + 7.91015625 Combine like terms: -5.9375 + 7.91015625 = 1.97265625 7.91015625 + -5.625x + x2 = 1.97265625 Factor a perfect square on the left side: (x + -2.8125)(x + -2.8125) = 1.97265625 Calculate the square root of the right side: 1.404512816 Break this problem into two subproblems by setting (x + -2.8125) equal to 1.404512816 and -1.404512816.Subproblem 1
x + -2.8125 = 1.404512816 Simplifying x + -2.8125 = 1.404512816 Reorder the terms: -2.8125 + x = 1.404512816 Solving -2.8125 + x = 1.404512816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = 1.404512816 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 1.404512816 + 2.8125 x = 1.404512816 + 2.8125 Combine like terms: 1.404512816 + 2.8125 = 4.217012816 x = 4.217012816 Simplifying x = 4.217012816Subproblem 2
x + -2.8125 = -1.404512816 Simplifying x + -2.8125 = -1.404512816 Reorder the terms: -2.8125 + x = -1.404512816 Solving -2.8125 + x = -1.404512816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = -1.404512816 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -1.404512816 + 2.8125 x = -1.404512816 + 2.8125 Combine like terms: -1.404512816 + 2.8125 = 1.407987184 x = 1.407987184 Simplifying x = 1.407987184Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.217012816, 1.407987184}
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