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Simplifying 3x2 + -18x + -39 = 5 Reorder the terms: -39 + -18x + 3x2 = 5 Solving -39 + -18x + 3x2 = 5 Solving for variable 'x'. Reorder the terms: -39 + -5 + -18x + 3x2 = 5 + -5 Combine like terms: -39 + -5 = -44 -44 + -18x + 3x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -44 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14.66666667 + -6x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + -6x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + -6x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + -6x + x2 = 0 + 14.66666667 -6x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 -6x + x2 = 14.66666667 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 = 14.66666667 + 9 Reorder the terms: 9 + -6x + x2 = 14.66666667 + 9 Combine like terms: 14.66666667 + 9 = 23.66666667 9 + -6x + x2 = 23.66666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 23.66666667 Calculate the square root of the right side: 4.86483984 Break this problem into two subproblems by setting (x + -3) equal to 4.86483984 and -4.86483984.Subproblem 1
x + -3 = 4.86483984 Simplifying x + -3 = 4.86483984 Reorder the terms: -3 + x = 4.86483984 Solving -3 + x = 4.86483984 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 = 4.86483984 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.86483984 + 3 x = 4.86483984 + 3 Combine like terms: 4.86483984 + 3 = 7.86483984 x = 7.86483984 Simplifying x = 7.86483984Subproblem 2
x + -3 = -4.86483984 Simplifying x + -3 = -4.86483984 Reorder the terms: -3 + x = -4.86483984 Solving -3 + x = -4.86483984 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 = -4.86483984 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.86483984 + 3 x = -4.86483984 + 3 Combine like terms: -4.86483984 + 3 = -1.86483984 x = -1.86483984 Simplifying x = -1.86483984Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.86483984, -1.86483984}
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