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Simplifying 0 = 6x2 + -3x + -20 Reorder the terms: 0 = -20 + -3x + 6x2 Solving 0 = -20 + -3x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 20 = 20 20 + 3x + -6x2 = -20 + -3x + 6x2 + 20 + 3x + -6x2 Reorder the terms: 20 + 3x + -6x2 = -20 + 20 + -3x + 3x + 6x2 + -6x2 Combine like terms: -20 + 20 = 0 20 + 3x + -6x2 = 0 + -3x + 3x + 6x2 + -6x2 20 + 3x + -6x2 = -3x + 3x + 6x2 + -6x2 Combine like terms: -3x + 3x = 0 20 + 3x + -6x2 = 0 + 6x2 + -6x2 20 + 3x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 20 + 3x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -3.333333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -0.5x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -0.5x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 3.333333333 -0.5x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -0.5x + x2 = 3.333333333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 3.333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 3.333333333 + 0.0625 Combine like terms: 3.333333333 + 0.0625 = 3.395833333 0.0625 + -0.5x + x2 = 3.395833333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 3.395833333 Calculate the square root of the right side: 1.842778699 Break this problem into two subproblems by setting (x + -0.25) equal to 1.842778699 and -1.842778699.Subproblem 1
x + -0.25 = 1.842778699 Simplifying x + -0.25 = 1.842778699 Reorder the terms: -0.25 + x = 1.842778699 Solving -0.25 + x = 1.842778699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.842778699 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.842778699 + 0.25 x = 1.842778699 + 0.25 Combine like terms: 1.842778699 + 0.25 = 2.092778699 x = 2.092778699 Simplifying x = 2.092778699Subproblem 2
x + -0.25 = -1.842778699 Simplifying x + -0.25 = -1.842778699 Reorder the terms: -0.25 + x = -1.842778699 Solving -0.25 + x = -1.842778699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.842778699 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.842778699 + 0.25 x = -1.842778699 + 0.25 Combine like terms: -1.842778699 + 0.25 = -1.592778699 x = -1.592778699 Simplifying x = -1.592778699Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.092778699, -1.592778699}
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