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Simplifying 9x2 + 3x + -56 = 56 Reorder the terms: -56 + 3x + 9x2 = 56 Solving -56 + 3x + 9x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + -56 + 3x + 9x2 = 56 + -56 Combine like terms: -56 + -56 = -112 -112 + 3x + 9x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -112 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -12.44444444 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '12.44444444' to each side of the equation. -12.44444444 + 0.3333333333x + 12.44444444 + x2 = 0 + 12.44444444 Reorder the terms: -12.44444444 + 12.44444444 + 0.3333333333x + x2 = 0 + 12.44444444 Combine like terms: -12.44444444 + 12.44444444 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 12.44444444 0.3333333333x + x2 = 0 + 12.44444444 Combine like terms: 0 + 12.44444444 = 12.44444444 0.3333333333x + x2 = 12.44444444 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 12.44444444 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 12.44444444 + 0.02777777779 Combine like terms: 12.44444444 + 0.02777777779 = 12.47222221779 0.02777777779 + 0.3333333333x + x2 = 12.47222221779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 12.47222221779 Calculate the square root of the right side: 3.531603349 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 3.531603349 and -3.531603349.Subproblem 1
x + 0.1666666667 = 3.531603349 Simplifying x + 0.1666666667 = 3.531603349 Reorder the terms: 0.1666666667 + x = 3.531603349 Solving 0.1666666667 + x = 3.531603349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 3.531603349 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 3.531603349 + -0.1666666667 x = 3.531603349 + -0.1666666667 Combine like terms: 3.531603349 + -0.1666666667 = 3.3649366823 x = 3.3649366823 Simplifying x = 3.3649366823Subproblem 2
x + 0.1666666667 = -3.531603349 Simplifying x + 0.1666666667 = -3.531603349 Reorder the terms: 0.1666666667 + x = -3.531603349 Solving 0.1666666667 + x = -3.531603349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -3.531603349 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -3.531603349 + -0.1666666667 x = -3.531603349 + -0.1666666667 Combine like terms: -3.531603349 + -0.1666666667 = -3.6982700157 x = -3.6982700157 Simplifying x = -3.6982700157Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3649366823, -3.6982700157}
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