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Simplifying 3x2 + -12x + -85 = 0 Reorder the terms: -85 + -12x + 3x2 = 0 Solving -85 + -12x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -28.33333333 + -4x + x2 = 0 Move the constant term to the right: Add '28.33333333' to each side of the equation. -28.33333333 + -4x + 28.33333333 + x2 = 0 + 28.33333333 Reorder the terms: -28.33333333 + 28.33333333 + -4x + x2 = 0 + 28.33333333 Combine like terms: -28.33333333 + 28.33333333 = 0.00000000 0.00000000 + -4x + x2 = 0 + 28.33333333 -4x + x2 = 0 + 28.33333333 Combine like terms: 0 + 28.33333333 = 28.33333333 -4x + x2 = 28.33333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 28.33333333 + 4 Reorder the terms: 4 + -4x + x2 = 28.33333333 + 4 Combine like terms: 28.33333333 + 4 = 32.33333333 4 + -4x + x2 = 32.33333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 32.33333333 Calculate the square root of the right side: 5.686240703 Break this problem into two subproblems by setting (x + -2) equal to 5.686240703 and -5.686240703.Subproblem 1
x + -2 = 5.686240703 Simplifying x + -2 = 5.686240703 Reorder the terms: -2 + x = 5.686240703 Solving -2 + x = 5.686240703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.686240703 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.686240703 + 2 x = 5.686240703 + 2 Combine like terms: 5.686240703 + 2 = 7.686240703 x = 7.686240703 Simplifying x = 7.686240703Subproblem 2
x + -2 = -5.686240703 Simplifying x + -2 = -5.686240703 Reorder the terms: -2 + x = -5.686240703 Solving -2 + x = -5.686240703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.686240703 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.686240703 + 2 x = -5.686240703 + 2 Combine like terms: -5.686240703 + 2 = -3.686240703 x = -3.686240703 Simplifying x = -3.686240703Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.686240703, -3.686240703}
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