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Simplifying 9x2 + 21x + -20 = 0 Reorder the terms: -20 + 21x + 9x2 = 0 Solving -20 + 21x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 2.333333333x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 2.333333333x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + 2.222222222 2.333333333x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 2.333333333x + x2 = 2.222222222 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 2.222222222 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 2.222222222 + 1.361111112 Combine like terms: 2.222222222 + 1.361111112 = 3.583333334 1.361111112 + 2.333333333x + x2 = 3.583333334 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 3.583333334 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.892969449 and -1.892969449.Subproblem 1
x + 1.166666667 = 1.892969449 Simplifying x + 1.166666667 = 1.892969449 Reorder the terms: 1.166666667 + x = 1.892969449 Solving 1.166666667 + x = 1.892969449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 1.892969449 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.892969449 + -1.166666667 x = 1.892969449 + -1.166666667 Combine like terms: 1.892969449 + -1.166666667 = 0.726302782 x = 0.726302782 Simplifying x = 0.726302782Subproblem 2
x + 1.166666667 = -1.892969449 Simplifying x + 1.166666667 = -1.892969449 Reorder the terms: 1.166666667 + x = -1.892969449 Solving 1.166666667 + x = -1.892969449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -1.892969449 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.892969449 + -1.166666667 x = -1.892969449 + -1.166666667 Combine like terms: -1.892969449 + -1.166666667 = -3.059636116 x = -3.059636116 Simplifying x = -3.059636116Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.726302782, -3.059636116}
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