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Simplifying 9x2 + -8 = -39x Reorder the terms: -8 + 9x2 = -39x Solving -8 + 9x2 = -39x Solving for variable 'x'. Reorder the terms: -8 + 39x + 9x2 = -39x + 39x Combine like terms: -39x + 39x = 0 -8 + 39x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 4.333333333x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 4.333333333x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 4.333333333x + x2 = 0 + 0.8888888889 4.333333333x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 4.333333333x + x2 = 0.8888888889 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = 0.8888888889 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 0.8888888889 + 4.694444446 Combine like terms: 0.8888888889 + 4.694444446 = 5.5833333349 4.694444446 + 4.333333333x + x2 = 5.5833333349 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 5.5833333349 Calculate the square root of the right side: 2.362907813 Break this problem into two subproblems by setting (x + 2.166666667) equal to 2.362907813 and -2.362907813.Subproblem 1
x + 2.166666667 = 2.362907813 Simplifying x + 2.166666667 = 2.362907813 Reorder the terms: 2.166666667 + x = 2.362907813 Solving 2.166666667 + x = 2.362907813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 2.362907813 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 2.362907813 + -2.166666667 x = 2.362907813 + -2.166666667 Combine like terms: 2.362907813 + -2.166666667 = 0.196241146 x = 0.196241146 Simplifying x = 0.196241146Subproblem 2
x + 2.166666667 = -2.362907813 Simplifying x + 2.166666667 = -2.362907813 Reorder the terms: 2.166666667 + x = -2.362907813 Solving 2.166666667 + x = -2.362907813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -2.362907813 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -2.362907813 + -2.166666667 x = -2.362907813 + -2.166666667 Combine like terms: -2.362907813 + -2.166666667 = -4.52957448 x = -4.52957448 Simplifying x = -4.52957448Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.196241146, -4.52957448}
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