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Simplifying 3x2 + 18x + -60 = 0 Reorder the terms: -60 + 18x + 3x2 = 0 Solving -60 + 18x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + 6x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-20 + 6x + x2)' equal to zero and attempt to solve: Simplifying -20 + 6x + x2 = 0 Solving -20 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 6x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 6x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 6x + x2 = 0 + 20 6x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 6x + x2 = 20 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 20 + 9 Reorder the terms: 9 + 6x + x2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + 6x + x2 = 29 Factor a perfect square on the left side: (x + 3)(x + 3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 3) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 3 = 5.385164807 Simplifying x + 3 = 5.385164807 Reorder the terms: 3 + x = 5.385164807 Solving 3 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.385164807 + -3 x = 5.385164807 + -3 Combine like terms: 5.385164807 + -3 = 2.385164807 x = 2.385164807 Simplifying x = 2.385164807Subproblem 2
x + 3 = -5.385164807 Simplifying x + 3 = -5.385164807 Reorder the terms: 3 + x = -5.385164807 Solving 3 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.385164807 + -3 x = -5.385164807 + -3 Combine like terms: -5.385164807 + -3 = -8.385164807 x = -8.385164807 Simplifying x = -8.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.385164807, -8.385164807}Solution
x = {2.385164807, -8.385164807}
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