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Simplifying 3x2 + 24x + -117 = 0 Reorder the terms: -117 + 24x + 3x2 = 0 Solving -117 + 24x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-39 + 8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-39 + 8x + x2)' equal to zero and attempt to solve: Simplifying -39 + 8x + x2 = 0 Solving -39 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 8x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 8x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 8x + x2 = 0 + 39 8x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 8x + x2 = 39 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 39 + 16 Reorder the terms: 16 + 8x + x2 = 39 + 16 Combine like terms: 39 + 16 = 55 16 + 8x + x2 = 55 Factor a perfect square on the left side: (x + 4)(x + 4) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + 4) equal to 7.416198487 and -7.416198487.Subproblem 1
x + 4 = 7.416198487 Simplifying x + 4 = 7.416198487 Reorder the terms: 4 + x = 7.416198487 Solving 4 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 7.416198487 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.416198487 + -4 x = 7.416198487 + -4 Combine like terms: 7.416198487 + -4 = 3.416198487 x = 3.416198487 Simplifying x = 3.416198487Subproblem 2
x + 4 = -7.416198487 Simplifying x + 4 = -7.416198487 Reorder the terms: 4 + x = -7.416198487 Solving 4 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -7.416198487 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.416198487 + -4 x = -7.416198487 + -4 Combine like terms: -7.416198487 + -4 = -11.416198487 x = -11.416198487 Simplifying x = -11.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.416198487, -11.416198487}Solution
x = {3.416198487, -11.416198487}
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