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Simplifying x = 3(3x + -5) * x + -19 Reorder the terms: x = 3(-5 + 3x) * x + -19 Reorder the terms for easier multiplication: x = 3x(-5 + 3x) + -19 x = (-5 * 3x + 3x * 3x) + -19 x = (-15x + 9x2) + -19 Reorder the terms: x = -19 + -15x + 9x2 Solving x = -19 + -15x + 9x2 Solving for variable 'x'. Reorder the terms: 19 + x + 15x + -9x2 = -19 + -15x + 9x2 + 19 + 15x + -9x2 Combine like terms: x + 15x = 16x 19 + 16x + -9x2 = -19 + -15x + 9x2 + 19 + 15x + -9x2 Reorder the terms: 19 + 16x + -9x2 = -19 + 19 + -15x + 15x + 9x2 + -9x2 Combine like terms: -19 + 19 = 0 19 + 16x + -9x2 = 0 + -15x + 15x + 9x2 + -9x2 19 + 16x + -9x2 = -15x + 15x + 9x2 + -9x2 Combine like terms: -15x + 15x = 0 19 + 16x + -9x2 = 0 + 9x2 + -9x2 19 + 16x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 19 + 16x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.111111111 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '2.111111111' to each side of the equation. -2.111111111 + -1.777777778x + 2.111111111 + x2 = 0 + 2.111111111 Reorder the terms: -2.111111111 + 2.111111111 + -1.777777778x + x2 = 0 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + -1.777777778x + x2 = 0 + 2.111111111 -1.777777778x + x2 = 0 + 2.111111111 Combine like terms: 0 + 2.111111111 = 2.111111111 -1.777777778x + x2 = 2.111111111 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 = 2.111111111 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 2.111111111 + 0.7901234570 Combine like terms: 2.111111111 + 0.7901234570 = 2.901234568 0.7901234570 + -1.777777778x + x2 = 2.901234568 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 2.901234568 Calculate the square root of the right side: 1.70330108 Break this problem into two subproblems by setting (x + -0.888888889) equal to 1.70330108 and -1.70330108.Subproblem 1
x + -0.888888889 = 1.70330108 Simplifying x + -0.888888889 = 1.70330108 Reorder the terms: -0.888888889 + x = 1.70330108 Solving -0.888888889 + x = 1.70330108 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 = 1.70330108 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 1.70330108 + 0.888888889 x = 1.70330108 + 0.888888889 Combine like terms: 1.70330108 + 0.888888889 = 2.592189969 x = 2.592189969 Simplifying x = 2.592189969Subproblem 2
x + -0.888888889 = -1.70330108 Simplifying x + -0.888888889 = -1.70330108 Reorder the terms: -0.888888889 + x = -1.70330108 Solving -0.888888889 + x = -1.70330108 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 = -1.70330108 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -1.70330108 + 0.888888889 x = -1.70330108 + 0.888888889 Combine like terms: -1.70330108 + 0.888888889 = -0.814412191 x = -0.814412191 Simplifying x = -0.814412191Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.592189969, -0.814412191}
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