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Simplifying 3(x2 + 18x + 81) = 54 Reorder the terms: 3(81 + 18x + x2) = 54 (81 * 3 + 18x * 3 + x2 * 3) = 54 (243 + 54x + 3x2) = 54 Solving 243 + 54x + 3x2 = 54 Solving for variable 'x'. Reorder the terms: 243 + -54 + 54x + 3x2 = 54 + -54 Combine like terms: 243 + -54 = 189 189 + 54x + 3x2 = 54 + -54 Combine like terms: 54 + -54 = 0 189 + 54x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(63 + 18x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(63 + 18x + x2)' equal to zero and attempt to solve: Simplifying 63 + 18x + x2 = 0 Solving 63 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 18x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + 18x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 18x + x2 = 0 + -63 18x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 18x + x2 = -63 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 = -63 + 81 Reorder the terms: 81 + 18x + x2 = -63 + 81 Combine like terms: -63 + 81 = 18 81 + 18x + x2 = 18 Factor a perfect square on the left side: (x + 9)(x + 9) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 9) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 9 = 4.242640687 Simplifying x + 9 = 4.242640687 Reorder the terms: 9 + x = 4.242640687 Solving 9 + x = 4.242640687 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 = 4.242640687 + -9 Combine like terms: 9 + -9 = 0 0 + x = 4.242640687 + -9 x = 4.242640687 + -9 Combine like terms: 4.242640687 + -9 = -4.757359313 x = -4.757359313 Simplifying x = -4.757359313Subproblem 2
x + 9 = -4.242640687 Simplifying x + 9 = -4.242640687 Reorder the terms: 9 + x = -4.242640687 Solving 9 + x = -4.242640687 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 = -4.242640687 + -9 Combine like terms: 9 + -9 = 0 0 + x = -4.242640687 + -9 x = -4.242640687 + -9 Combine like terms: -4.242640687 + -9 = -13.242640687 x = -13.242640687 Simplifying x = -13.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.757359313, -13.242640687}Solution
x = {-4.757359313, -13.242640687}
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