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Simplifying 3x2 + 21x + 20 = 0 Reorder the terms: 20 + 21x + 3x2 = 0 Solving 20 + 21x + 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'. 6.666666667 + 7x + x2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + 7x + -6.666666667 + x2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + 7x + x2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + 7x + x2 = 0 + -6.666666667 7x + x2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 7x + x2 = -6.666666667 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -6.666666667 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -6.666666667 + 12.25 Combine like terms: -6.666666667 + 12.25 = 5.583333333 12.25 + 7x + x2 = 5.583333333 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 5.583333333 Calculate the square root of the right side: 2.362907813 Break this problem into two subproblems by setting (x + 3.5) equal to 2.362907813 and -2.362907813.Subproblem 1
x + 3.5 = 2.362907813 Simplifying x + 3.5 = 2.362907813 Reorder the terms: 3.5 + x = 2.362907813 Solving 3.5 + x = 2.362907813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.362907813 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.362907813 + -3.5 x = 2.362907813 + -3.5 Combine like terms: 2.362907813 + -3.5 = -1.137092187 x = -1.137092187 Simplifying x = -1.137092187Subproblem 2
x + 3.5 = -2.362907813 Simplifying x + 3.5 = -2.362907813 Reorder the terms: 3.5 + x = -2.362907813 Solving 3.5 + x = -2.362907813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.362907813 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.362907813 + -3.5 x = -2.362907813 + -3.5 Combine like terms: -2.362907813 + -3.5 = -5.862907813 x = -5.862907813 Simplifying x = -5.862907813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.137092187, -5.862907813}
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