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Simplifying 6x2 + 3x = 20 Reorder the terms: 3x + 6x2 = 20 Solving 3x + 6x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 3x + 6x2 = 20 + -20 Combine like terms: 20 + -20 = 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 = 1.592778699 x = 1.592778699 Simplifying x = 1.592778699Subproblem 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 = -2.092778699 x = -2.092778699 Simplifying x = -2.092778699Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.592778699, -2.092778699}
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