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Simplifying 3x2 + -1x + -84 = 0 Reorder the terms: -84 + -1x + 3x2 = 0 Solving -84 + -1x + 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 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -0.3333333333x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -0.3333333333x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -0.3333333333x + x2 = 0 + 28 -0.3333333333x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -0.3333333333x + x2 = 28 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 28 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 28 + 0.02777777779 Combine like terms: 28 + 0.02777777779 = 28.02777777779 0.02777777779 + -0.3333333333x + x2 = 28.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 28.02777777779 Calculate the square root of the right side: 5.294126725 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 5.294126725 and -5.294126725.Subproblem 1
x + -0.1666666667 = 5.294126725 Simplifying x + -0.1666666667 = 5.294126725 Reorder the terms: -0.1666666667 + x = 5.294126725 Solving -0.1666666667 + x = 5.294126725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 5.294126725 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 5.294126725 + 0.1666666667 x = 5.294126725 + 0.1666666667 Combine like terms: 5.294126725 + 0.1666666667 = 5.4607933917 x = 5.4607933917 Simplifying x = 5.4607933917Subproblem 2
x + -0.1666666667 = -5.294126725 Simplifying x + -0.1666666667 = -5.294126725 Reorder the terms: -0.1666666667 + x = -5.294126725 Solving -0.1666666667 + x = -5.294126725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -5.294126725 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -5.294126725 + 0.1666666667 x = -5.294126725 + 0.1666666667 Combine like terms: -5.294126725 + 0.1666666667 = -5.1274600583 x = -5.1274600583 Simplifying x = -5.1274600583Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4607933917, -5.1274600583}
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