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Simplifying 9x2 + 18x + -85 = -3 Reorder the terms: -85 + 18x + 9x2 = -3 Solving -85 + 18x + 9x2 = -3 Solving for variable 'x'. Reorder the terms: -85 + 3 + 18x + 9x2 = -3 + 3 Combine like terms: -85 + 3 = -82 -82 + 18x + 9x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -82 + 18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -9.111111111 + 2x + x2 = 0 Move the constant term to the right: Add '9.111111111' to each side of the equation. -9.111111111 + 2x + 9.111111111 + x2 = 0 + 9.111111111 Reorder the terms: -9.111111111 + 9.111111111 + 2x + x2 = 0 + 9.111111111 Combine like terms: -9.111111111 + 9.111111111 = 0.000000000 0.000000000 + 2x + x2 = 0 + 9.111111111 2x + x2 = 0 + 9.111111111 Combine like terms: 0 + 9.111111111 = 9.111111111 2x + x2 = 9.111111111 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 9.111111111 + 1 Reorder the terms: 1 + 2x + x2 = 9.111111111 + 1 Combine like terms: 9.111111111 + 1 = 10.111111111 1 + 2x + x2 = 10.111111111 Factor a perfect square on the left side: (x + 1)(x + 1) = 10.111111111 Calculate the square root of the right side: 3.179797338 Break this problem into two subproblems by setting (x + 1) equal to 3.179797338 and -3.179797338.Subproblem 1
x + 1 = 3.179797338 Simplifying x + 1 = 3.179797338 Reorder the terms: 1 + x = 3.179797338 Solving 1 + x = 3.179797338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.179797338 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.179797338 + -1 x = 3.179797338 + -1 Combine like terms: 3.179797338 + -1 = 2.179797338 x = 2.179797338 Simplifying x = 2.179797338Subproblem 2
x + 1 = -3.179797338 Simplifying x + 1 = -3.179797338 Reorder the terms: 1 + x = -3.179797338 Solving 1 + x = -3.179797338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.179797338 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.179797338 + -1 x = -3.179797338 + -1 Combine like terms: -3.179797338 + -1 = -4.179797338 x = -4.179797338 Simplifying x = -4.179797338Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.179797338, -4.179797338}
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