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Simplifying (x + 18)(x) = (3) Reorder the terms: (18 + x)(x) = (3) Reorder the terms for easier multiplication: x(18 + x) = (3) (18 * x + x * x) = (3) (18x + x2) = (3) 18x + x2 = 3 Solving 18x + x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 18x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 18x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 18x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 18x + x2 = 0 + 3 18x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 18x + x2 = 3 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 = 3 + 81 Reorder the terms: 81 + 18x + x2 = 3 + 81 Combine like terms: 3 + 81 = 84 81 + 18x + x2 = 84 Factor a perfect square on the left side: (x + 9)(x + 9) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + 9) equal to 9.16515139 and -9.16515139.Subproblem 1
x + 9 = 9.16515139 Simplifying x + 9 = 9.16515139 Reorder the terms: 9 + x = 9.16515139 Solving 9 + x = 9.16515139 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 = 9.16515139 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.16515139 + -9 x = 9.16515139 + -9 Combine like terms: 9.16515139 + -9 = 0.16515139 x = 0.16515139 Simplifying x = 0.16515139Subproblem 2
x + 9 = -9.16515139 Simplifying x + 9 = -9.16515139 Reorder the terms: 9 + x = -9.16515139 Solving 9 + x = -9.16515139 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 = -9.16515139 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.16515139 + -9 x = -9.16515139 + -9 Combine like terms: -9.16515139 + -9 = -18.16515139 x = -18.16515139 Simplifying x = -18.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.16515139, -18.16515139}
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