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Simplifying 3x2 + 54x + 183 = 0 Reorder the terms: 183 + 54x + 3x2 = 0 Solving 183 + 54x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(61 + 18x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(61 + 18x + x2)' equal to zero and attempt to solve: Simplifying 61 + 18x + x2 = 0 Solving 61 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-61' to each side of the equation. 61 + 18x + -61 + x2 = 0 + -61 Reorder the terms: 61 + -61 + 18x + x2 = 0 + -61 Combine like terms: 61 + -61 = 0 0 + 18x + x2 = 0 + -61 18x + x2 = 0 + -61 Combine like terms: 0 + -61 = -61 18x + x2 = -61 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 = -61 + 81 Reorder the terms: 81 + 18x + x2 = -61 + 81 Combine like terms: -61 + 81 = 20 81 + 18x + x2 = 20 Factor a perfect square on the left side: (x + 9)(x + 9) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 9) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 9 = 4.472135955 Simplifying x + 9 = 4.472135955 Reorder the terms: 9 + x = 4.472135955 Solving 9 + x = 4.472135955 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 = 4.472135955 + -9 Combine like terms: 9 + -9 = 0 0 + x = 4.472135955 + -9 x = 4.472135955 + -9 Combine like terms: 4.472135955 + -9 = -4.527864045 x = -4.527864045 Simplifying x = -4.527864045Subproblem 2
x + 9 = -4.472135955 Simplifying x + 9 = -4.472135955 Reorder the terms: 9 + x = -4.472135955 Solving 9 + x = -4.472135955 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 = -4.472135955 + -9 Combine like terms: 9 + -9 = 0 0 + x = -4.472135955 + -9 x = -4.472135955 + -9 Combine like terms: -4.472135955 + -9 = -13.472135955 x = -13.472135955 Simplifying x = -13.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.527864045, -13.472135955}Solution
x = {-4.527864045, -13.472135955}
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