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Simplifying x2 + 18x + 18 = 25 Reorder the terms: 18 + 18x + x2 = 25 Solving 18 + 18x + x2 = 25 Solving for variable 'x'. Reorder the terms: 18 + -25 + 18x + x2 = 25 + -25 Combine like terms: 18 + -25 = -7 -7 + 18x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -7 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 18x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 18x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 18x + x2 = 0 + 7 18x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 18x + x2 = 7 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 = 7 + 81 Reorder the terms: 81 + 18x + x2 = 7 + 81 Combine like terms: 7 + 81 = 88 81 + 18x + x2 = 88 Factor a perfect square on the left side: (x + 9)(x + 9) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + 9) equal to 9.38083152 and -9.38083152.Subproblem 1
x + 9 = 9.38083152 Simplifying x + 9 = 9.38083152 Reorder the terms: 9 + x = 9.38083152 Solving 9 + x = 9.38083152 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 = 9.38083152 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.38083152 + -9 x = 9.38083152 + -9 Combine like terms: 9.38083152 + -9 = 0.38083152 x = 0.38083152 Simplifying x = 0.38083152Subproblem 2
x + 9 = -9.38083152 Simplifying x + 9 = -9.38083152 Reorder the terms: 9 + x = -9.38083152 Solving 9 + x = -9.38083152 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 = -9.38083152 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.38083152 + -9 x = -9.38083152 + -9 Combine like terms: -9.38083152 + -9 = -18.38083152 x = -18.38083152 Simplifying x = -18.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.38083152, -18.38083152}
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