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Simplifying 3x2 + -36x + -27 = 0 Reorder the terms: -27 + -36x + 3x2 = 0 Solving -27 + -36x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + -12x + x2)' equal to zero and attempt to solve: Simplifying -9 + -12x + x2 = 0 Solving -9 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -12x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -12x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -12x + x2 = 0 + 9 -12x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -12x + x2 = 9 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 = 9 + 36 Reorder the terms: 36 + -12x + x2 = 9 + 36 Combine like terms: 9 + 36 = 45 36 + -12x + x2 = 45 Factor a perfect square on the left side: (x + -6)(x + -6) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -6) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -6 = 6.708203933 Simplifying x + -6 = 6.708203933 Reorder the terms: -6 + x = 6.708203933 Solving -6 + x = 6.708203933 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 = 6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.708203933 + 6 x = 6.708203933 + 6 Combine like terms: 6.708203933 + 6 = 12.708203933 x = 12.708203933 Simplifying x = 12.708203933Subproblem 2
x + -6 = -6.708203933 Simplifying x + -6 = -6.708203933 Reorder the terms: -6 + x = -6.708203933 Solving -6 + x = -6.708203933 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 = -6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.708203933 + 6 x = -6.708203933 + 6 Combine like terms: -6.708203933 + 6 = -0.708203933 x = -0.708203933 Simplifying x = -0.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.708203933, -0.708203933}Solution
x = {12.708203933, -0.708203933}
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