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Simplifying 3x2 + 36x + 21 = 0 Reorder the terms: 21 + 36x + 3x2 = 0 Solving 21 + 36x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + 12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 12x + x2)' equal to zero and attempt to solve: Simplifying 7 + 12x + x2 = 0 Solving 7 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 12x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 12x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 12x + x2 = 0 + -7 12x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 12x + x2 = -7 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -7 + 36 Reorder the terms: 36 + 12x + x2 = -7 + 36 Combine like terms: -7 + 36 = 29 36 + 12x + x2 = 29 Factor a perfect square on the left side: (x + 6)(x + 6) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 6) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 6 = 5.385164807 Simplifying x + 6 = 5.385164807 Reorder the terms: 6 + x = 5.385164807 Solving 6 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.385164807 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.385164807 + -6 x = 5.385164807 + -6 Combine like terms: 5.385164807 + -6 = -0.614835193 x = -0.614835193 Simplifying x = -0.614835193Subproblem 2
x + 6 = -5.385164807 Simplifying x + 6 = -5.385164807 Reorder the terms: 6 + x = -5.385164807 Solving 6 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.385164807 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.385164807 + -6 x = -5.385164807 + -6 Combine like terms: -5.385164807 + -6 = -11.385164807 x = -11.385164807 Simplifying x = -11.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.614835193, -11.385164807}Solution
x = {-0.614835193, -11.385164807}
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