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Simplifying 0.0018x2 + -0.32x + 92 = 85 Reorder the terms: 92 + -0.32x + 0.0018x2 = 85 Solving 92 + -0.32x + 0.0018x2 = 85 Solving for variable 'x'. Reorder the terms: 92 + -85 + -0.32x + 0.0018x2 = 85 + -85 Combine like terms: 92 + -85 = 7 7 + -0.32x + 0.0018x2 = 85 + -85 Combine like terms: 85 + -85 = 0 7 + -0.32x + 0.0018x2 = 0 Begin completing the square. Divide all terms by 0.0018 the coefficient of the squared term: Divide each side by '0.0018'. 3888.888889 + -177.7777778x + x2 = 0 Move the constant term to the right: Add '-3888.888889' to each side of the equation. 3888.888889 + -177.7777778x + -3888.888889 + x2 = 0 + -3888.888889 Reorder the terms: 3888.888889 + -3888.888889 + -177.7777778x + x2 = 0 + -3888.888889 Combine like terms: 3888.888889 + -3888.888889 = 0.000000 0.000000 + -177.7777778x + x2 = 0 + -3888.888889 -177.7777778x + x2 = 0 + -3888.888889 Combine like terms: 0 + -3888.888889 = -3888.888889 -177.7777778x + x2 = -3888.888889 The x term is -177.7777778x. Take half its coefficient (-88.8888889). Square it (7901.234570) and add it to both sides. Add '7901.234570' to each side of the equation. -177.7777778x + 7901.234570 + x2 = -3888.888889 + 7901.234570 Reorder the terms: 7901.234570 + -177.7777778x + x2 = -3888.888889 + 7901.234570 Combine like terms: -3888.888889 + 7901.234570 = 4012.345681 7901.234570 + -177.7777778x + x2 = 4012.345681 Factor a perfect square on the left side: (x + -88.8888889)(x + -88.8888889) = 4012.345681 Calculate the square root of the right side: 63.343079188 Break this problem into two subproblems by setting (x + -88.8888889) equal to 63.343079188 and -63.343079188.Subproblem 1
x + -88.8888889 = 63.343079188 Simplifying x + -88.8888889 = 63.343079188 Reorder the terms: -88.8888889 + x = 63.343079188 Solving -88.8888889 + x = 63.343079188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '88.8888889' to each side of the equation. -88.8888889 + 88.8888889 + x = 63.343079188 + 88.8888889 Combine like terms: -88.8888889 + 88.8888889 = 0.0000000 0.0000000 + x = 63.343079188 + 88.8888889 x = 63.343079188 + 88.8888889 Combine like terms: 63.343079188 + 88.8888889 = 152.231968088 x = 152.231968088 Simplifying x = 152.231968088Subproblem 2
x + -88.8888889 = -63.343079188 Simplifying x + -88.8888889 = -63.343079188 Reorder the terms: -88.8888889 + x = -63.343079188 Solving -88.8888889 + x = -63.343079188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '88.8888889' to each side of the equation. -88.8888889 + 88.8888889 + x = -63.343079188 + 88.8888889 Combine like terms: -88.8888889 + 88.8888889 = 0.0000000 0.0000000 + x = -63.343079188 + 88.8888889 x = -63.343079188 + 88.8888889 Combine like terms: -63.343079188 + 88.8888889 = 25.545809712 x = 25.545809712 Simplifying x = 25.545809712Solution
The solution to the problem is based on the solutions from the subproblems. x = {152.231968088, 25.545809712}
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