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Simplifying 3x2 + -36x + -3 = 0 Reorder the terms: -3 + -36x + 3x2 = 0 Solving -3 + -36x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -12x + x2)' equal to zero and attempt to solve: Simplifying -1 + -12x + x2 = 0 Solving -1 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -12x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -12x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -12x + x2 = 0 + 1 -12x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -12x + x2 = 1 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 = 1 + 36 Reorder the terms: 36 + -12x + x2 = 1 + 36 Combine like terms: 1 + 36 = 37 36 + -12x + x2 = 37 Factor a perfect square on the left side: (x + -6)(x + -6) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -6) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -6 = 6.08276253 Simplifying x + -6 = 6.08276253 Reorder the terms: -6 + x = 6.08276253 Solving -6 + x = 6.08276253 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 = 6.08276253 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.08276253 + 6 x = 6.08276253 + 6 Combine like terms: 6.08276253 + 6 = 12.08276253 x = 12.08276253 Simplifying x = 12.08276253Subproblem 2
x + -6 = -6.08276253 Simplifying x + -6 = -6.08276253 Reorder the terms: -6 + x = -6.08276253 Solving -6 + x = -6.08276253 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 = -6.08276253 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.08276253 + 6 x = -6.08276253 + 6 Combine like terms: -6.08276253 + 6 = -0.08276253 x = -0.08276253 Simplifying x = -0.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.08276253, -0.08276253}Solution
x = {12.08276253, -0.08276253}
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