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Simplifying 6x2 + -72x + -18 = 0 Reorder the terms: -18 + -72x + 6x2 = 0 Solving -18 + -72x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + -12x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + -12x + x2)' equal to zero and attempt to solve: Simplifying -3 + -12x + x2 = 0 Solving -3 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -12x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -12x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -12x + x2 = 0 + 3 -12x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -12x + x2 = 3 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 = 3 + 36 Reorder the terms: 36 + -12x + x2 = 3 + 36 Combine like terms: 3 + 36 = 39 36 + -12x + x2 = 39 Factor a perfect square on the left side: (x + -6)(x + -6) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -6) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -6 = 6.244997998 Simplifying x + -6 = 6.244997998 Reorder the terms: -6 + x = 6.244997998 Solving -6 + x = 6.244997998 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 = 6.244997998 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.244997998 + 6 x = 6.244997998 + 6 Combine like terms: 6.244997998 + 6 = 12.244997998 x = 12.244997998 Simplifying x = 12.244997998Subproblem 2
x + -6 = -6.244997998 Simplifying x + -6 = -6.244997998 Reorder the terms: -6 + x = -6.244997998 Solving -6 + x = -6.244997998 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 = -6.244997998 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.244997998 + 6 x = -6.244997998 + 6 Combine like terms: -6.244997998 + 6 = -0.244997998 x = -0.244997998 Simplifying x = -0.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.244997998, -0.244997998}Solution
x = {12.244997998, -0.244997998}
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