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Simplifying 18x2 + -95x + 93.5 = 0 Reorder the terms: 93.5 + -95x + 18x2 = 0 Solving 93.5 + -95x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 5.194444444 + -5.277777778x + x2 = 0 Move the constant term to the right: Add '-5.194444444' to each side of the equation. 5.194444444 + -5.277777778x + -5.194444444 + x2 = 0 + -5.194444444 Reorder the terms: 5.194444444 + -5.194444444 + -5.277777778x + x2 = 0 + -5.194444444 Combine like terms: 5.194444444 + -5.194444444 = 0.000000000 0.000000000 + -5.277777778x + x2 = 0 + -5.194444444 -5.277777778x + x2 = 0 + -5.194444444 Combine like terms: 0 + -5.194444444 = -5.194444444 -5.277777778x + x2 = -5.194444444 The x term is -5.277777778x. Take half its coefficient (-2.638888889). Square it (6.963734568) and add it to both sides. Add '6.963734568' to each side of the equation. -5.277777778x + 6.963734568 + x2 = -5.194444444 + 6.963734568 Reorder the terms: 6.963734568 + -5.277777778x + x2 = -5.194444444 + 6.963734568 Combine like terms: -5.194444444 + 6.963734568 = 1.769290124 6.963734568 + -5.277777778x + x2 = 1.769290124 Factor a perfect square on the left side: (x + -2.638888889)(x + -2.638888889) = 1.769290124 Calculate the square root of the right side: 1.330146655 Break this problem into two subproblems by setting (x + -2.638888889) equal to 1.330146655 and -1.330146655.Subproblem 1
x + -2.638888889 = 1.330146655 Simplifying x + -2.638888889 = 1.330146655 Reorder the terms: -2.638888889 + x = 1.330146655 Solving -2.638888889 + x = 1.330146655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.638888889' to each side of the equation. -2.638888889 + 2.638888889 + x = 1.330146655 + 2.638888889 Combine like terms: -2.638888889 + 2.638888889 = 0.000000000 0.000000000 + x = 1.330146655 + 2.638888889 x = 1.330146655 + 2.638888889 Combine like terms: 1.330146655 + 2.638888889 = 3.969035544 x = 3.969035544 Simplifying x = 3.969035544Subproblem 2
x + -2.638888889 = -1.330146655 Simplifying x + -2.638888889 = -1.330146655 Reorder the terms: -2.638888889 + x = -1.330146655 Solving -2.638888889 + x = -1.330146655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.638888889' to each side of the equation. -2.638888889 + 2.638888889 + x = -1.330146655 + 2.638888889 Combine like terms: -2.638888889 + 2.638888889 = 0.000000000 0.000000000 + x = -1.330146655 + 2.638888889 x = -1.330146655 + 2.638888889 Combine like terms: -1.330146655 + 2.638888889 = 1.308742234 x = 1.308742234 Simplifying x = 1.308742234Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.969035544, 1.308742234}
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