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Simplifying 9x2 + -16x + -324 = 0 Reorder the terms: -324 + -16x + 9x2 = 0 Solving -324 + -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'. -36 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -1.777777778x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -1.777777778x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1.777777778x + x2 = 0 + 36 -1.777777778x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1.777777778x + x2 = 36 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 = 36 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 36 + 0.7901234570 Combine like terms: 36 + 0.7901234570 = 36.790123457 0.7901234570 + -1.777777778x + x2 = 36.790123457 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 36.790123457 Calculate the square root of the right side: 6.065486251 Break this problem into two subproblems by setting (x + -0.888888889) equal to 6.065486251 and -6.065486251.Subproblem 1
x + -0.888888889 = 6.065486251 Simplifying x + -0.888888889 = 6.065486251 Reorder the terms: -0.888888889 + x = 6.065486251 Solving -0.888888889 + x = 6.065486251 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 = 6.065486251 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 6.065486251 + 0.888888889 x = 6.065486251 + 0.888888889 Combine like terms: 6.065486251 + 0.888888889 = 6.95437514 x = 6.95437514 Simplifying x = 6.95437514Subproblem 2
x + -0.888888889 = -6.065486251 Simplifying x + -0.888888889 = -6.065486251 Reorder the terms: -0.888888889 + x = -6.065486251 Solving -0.888888889 + x = -6.065486251 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 = -6.065486251 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -6.065486251 + 0.888888889 x = -6.065486251 + 0.888888889 Combine like terms: -6.065486251 + 0.888888889 = -5.176597362 x = -5.176597362 Simplifying x = -5.176597362Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.95437514, -5.176597362}
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