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Simplifying 3x2 + -36x + -144 = 0 Reorder the terms: -144 + -36x + 3x2 = 0 Solving -144 + -36x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-48 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-48 + -12x + x2)' equal to zero and attempt to solve: Simplifying -48 + -12x + x2 = 0 Solving -48 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -12x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -12x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -12x + x2 = 0 + 48 -12x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -12x + x2 = 48 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 = 48 + 36 Reorder the terms: 36 + -12x + x2 = 48 + 36 Combine like terms: 48 + 36 = 84 36 + -12x + x2 = 84 Factor a perfect square on the left side: (x + -6)(x + -6) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + -6) equal to 9.16515139 and -9.16515139.Subproblem 1
x + -6 = 9.16515139 Simplifying x + -6 = 9.16515139 Reorder the terms: -6 + x = 9.16515139 Solving -6 + x = 9.16515139 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 = 9.16515139 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.16515139 + 6 x = 9.16515139 + 6 Combine like terms: 9.16515139 + 6 = 15.16515139 x = 15.16515139 Simplifying x = 15.16515139Subproblem 2
x + -6 = -9.16515139 Simplifying x + -6 = -9.16515139 Reorder the terms: -6 + x = -9.16515139 Solving -6 + x = -9.16515139 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 = -9.16515139 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.16515139 + 6 x = -9.16515139 + 6 Combine like terms: -9.16515139 + 6 = -3.16515139 x = -3.16515139 Simplifying x = -3.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.16515139, -3.16515139}Solution
x = {15.16515139, -3.16515139}
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