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Simplifying 3x2 + 135x + 85 = 0 Reorder the terms: 85 + 135x + 3x2 = 0 Solving 85 + 135x + 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 + 45x + x2 = 0 Move the constant term to the right: Add '-28.33333333' to each side of the equation. 28.33333333 + 45x + -28.33333333 + x2 = 0 + -28.33333333 Reorder the terms: 28.33333333 + -28.33333333 + 45x + x2 = 0 + -28.33333333 Combine like terms: 28.33333333 + -28.33333333 = 0.00000000 0.00000000 + 45x + x2 = 0 + -28.33333333 45x + x2 = 0 + -28.33333333 Combine like terms: 0 + -28.33333333 = -28.33333333 45x + x2 = -28.33333333 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = -28.33333333 + 506.25 Reorder the terms: 506.25 + 45x + x2 = -28.33333333 + 506.25 Combine like terms: -28.33333333 + 506.25 = 477.91666667 506.25 + 45x + x2 = 477.91666667 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 477.91666667 Calculate the square root of the right side: 21.861305237 Break this problem into two subproblems by setting (x + 22.5) equal to 21.861305237 and -21.861305237.Subproblem 1
x + 22.5 = 21.861305237 Simplifying x + 22.5 = 21.861305237 Reorder the terms: 22.5 + x = 21.861305237 Solving 22.5 + x = 21.861305237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 21.861305237 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 21.861305237 + -22.5 x = 21.861305237 + -22.5 Combine like terms: 21.861305237 + -22.5 = -0.638694763 x = -0.638694763 Simplifying x = -0.638694763Subproblem 2
x + 22.5 = -21.861305237 Simplifying x + 22.5 = -21.861305237 Reorder the terms: 22.5 + x = -21.861305237 Solving 22.5 + x = -21.861305237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -21.861305237 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -21.861305237 + -22.5 x = -21.861305237 + -22.5 Combine like terms: -21.861305237 + -22.5 = -44.361305237 x = -44.361305237 Simplifying x = -44.361305237Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.638694763, -44.361305237}
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