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Simplifying 9x2 + -16x + -256 = 0 Reorder the terms: -256 + -16x + 9x2 = 0 Solving -256 + -16x + 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'. -28.44444444 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '28.44444444' to each side of the equation. -28.44444444 + -1.777777778x + 28.44444444 + x2 = 0 + 28.44444444 Reorder the terms: -28.44444444 + 28.44444444 + -1.777777778x + x2 = 0 + 28.44444444 Combine like terms: -28.44444444 + 28.44444444 = 0.00000000 0.00000000 + -1.777777778x + x2 = 0 + 28.44444444 -1.777777778x + x2 = 0 + 28.44444444 Combine like terms: 0 + 28.44444444 = 28.44444444 -1.777777778x + x2 = 28.44444444 The x term is -1.777777778x. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778x + 0.7901234570 + x2 = 28.44444444 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 28.44444444 + 0.7901234570 Combine like terms: 28.44444444 + 0.7901234570 = 29.234567897 0.7901234570 + -1.777777778x + x2 = 29.234567897 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 29.234567897 Calculate the square root of the right side: 5.406900027 Break this problem into two subproblems by setting (x + -0.888888889) equal to 5.406900027 and -5.406900027.Subproblem 1
x + -0.888888889 = 5.406900027 Simplifying x + -0.888888889 = 5.406900027 Reorder the terms: -0.888888889 + x = 5.406900027 Solving -0.888888889 + x = 5.406900027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = 5.406900027 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 5.406900027 + 0.888888889 x = 5.406900027 + 0.888888889 Combine like terms: 5.406900027 + 0.888888889 = 6.295788916 x = 6.295788916 Simplifying x = 6.295788916Subproblem 2
x + -0.888888889 = -5.406900027 Simplifying x + -0.888888889 = -5.406900027 Reorder the terms: -0.888888889 + x = -5.406900027 Solving -0.888888889 + x = -5.406900027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = -5.406900027 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -5.406900027 + 0.888888889 x = -5.406900027 + 0.888888889 Combine like terms: -5.406900027 + 0.888888889 = -4.518011138 x = -4.518011138 Simplifying x = -4.518011138Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.295788916, -4.518011138}
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