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Simplifying x2 + 18x + 81 + -45 = 0 Reorder the terms: 81 + -45 + 18x + x2 = 0 Combine like terms: 81 + -45 = 36 36 + 18x + x2 = 0 Solving 36 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 18x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 18x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 18x + x2 = 0 + -36 18x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 18x + x2 = -36 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -36 + 81 Reorder the terms: 81 + 18x + x2 = -36 + 81 Combine like terms: -36 + 81 = 45 81 + 18x + x2 = 45 Factor a perfect square on the left side: (x + 9)(x + 9) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 9) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 9 = 6.708203933 Simplifying x + 9 = 6.708203933 Reorder the terms: 9 + x = 6.708203933 Solving 9 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 6.708203933 + -9 Combine like terms: 9 + -9 = 0 0 + x = 6.708203933 + -9 x = 6.708203933 + -9 Combine like terms: 6.708203933 + -9 = -2.291796067 x = -2.291796067 Simplifying x = -2.291796067Subproblem 2
x + 9 = -6.708203933 Simplifying x + 9 = -6.708203933 Reorder the terms: 9 + x = -6.708203933 Solving 9 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -6.708203933 + -9 Combine like terms: 9 + -9 = 0 0 + x = -6.708203933 + -9 x = -6.708203933 + -9 Combine like terms: -6.708203933 + -9 = -15.708203933 x = -15.708203933 Simplifying x = -15.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.291796067, -15.708203933}
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