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Simplifying 9x2 + 18x = 46 Reorder the terms: 18x + 9x2 = 46 Solving 18x + 9x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 18x + 9x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.111111111 + 2x + x2 = 0 Move the constant term to the right: Add '5.111111111' to each side of the equation. -5.111111111 + 2x + 5.111111111 + x2 = 0 + 5.111111111 Reorder the terms: -5.111111111 + 5.111111111 + 2x + x2 = 0 + 5.111111111 Combine like terms: -5.111111111 + 5.111111111 = 0.000000000 0.000000000 + 2x + x2 = 0 + 5.111111111 2x + x2 = 0 + 5.111111111 Combine like terms: 0 + 5.111111111 = 5.111111111 2x + x2 = 5.111111111 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 = 5.111111111 + 1 Reorder the terms: 1 + 2x + x2 = 5.111111111 + 1 Combine like terms: 5.111111111 + 1 = 6.111111111 1 + 2x + x2 = 6.111111111 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.111111111 Calculate the square root of the right side: 2.472066162 Break this problem into two subproblems by setting (x + 1) equal to 2.472066162 and -2.472066162.Subproblem 1
x + 1 = 2.472066162 Simplifying x + 1 = 2.472066162 Reorder the terms: 1 + x = 2.472066162 Solving 1 + x = 2.472066162 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 = 2.472066162 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.472066162 + -1 x = 2.472066162 + -1 Combine like terms: 2.472066162 + -1 = 1.472066162 x = 1.472066162 Simplifying x = 1.472066162Subproblem 2
x + 1 = -2.472066162 Simplifying x + 1 = -2.472066162 Reorder the terms: 1 + x = -2.472066162 Solving 1 + x = -2.472066162 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 = -2.472066162 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.472066162 + -1 x = -2.472066162 + -1 Combine like terms: -2.472066162 + -1 = -3.472066162 x = -3.472066162 Simplifying x = -3.472066162Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.472066162, -3.472066162}
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