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Simplifying 3x2 + 18x + -39 = 0 Reorder the terms: -39 + 18x + 3x2 = 0 Solving -39 + 18x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + 6x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + 6x + x2)' equal to zero and attempt to solve: Simplifying -13 + 6x + x2 = 0 Solving -13 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 6x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 6x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 6x + x2 = 0 + 13 6x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 6x + x2 = 13 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 13 + 9 Reorder the terms: 9 + 6x + x2 = 13 + 9 Combine like terms: 13 + 9 = 22 9 + 6x + x2 = 22 Factor a perfect square on the left side: (x + 3)(x + 3) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 3) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 3 = 4.69041576 Simplifying x + 3 = 4.69041576 Reorder the terms: 3 + x = 4.69041576 Solving 3 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.69041576 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.69041576 + -3 x = 4.69041576 + -3 Combine like terms: 4.69041576 + -3 = 1.69041576 x = 1.69041576 Simplifying x = 1.69041576Subproblem 2
x + 3 = -4.69041576 Simplifying x + 3 = -4.69041576 Reorder the terms: 3 + x = -4.69041576 Solving 3 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.69041576 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.69041576 + -3 x = -4.69041576 + -3 Combine like terms: -4.69041576 + -3 = -7.69041576 x = -7.69041576 Simplifying x = -7.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.69041576, -7.69041576}Solution
x = {1.69041576, -7.69041576}
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