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Simplifying 3x(3x + -2) + -1x + -8 = 10 Reorder the terms: 3x(-2 + 3x) + -1x + -8 = 10 (-2 * 3x + 3x * 3x) + -1x + -8 = 10 (-6x + 9x2) + -1x + -8 = 10 Reorder the terms: -8 + -6x + -1x + 9x2 = 10 Combine like terms: -6x + -1x = -7x -8 + -7x + 9x2 = 10 Solving -8 + -7x + 9x2 = 10 Solving for variable 'x'. Reorder the terms: -8 + -10 + -7x + 9x2 = 10 + -10 Combine like terms: -8 + -10 = -18 -18 + -7x + 9x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -18 + -7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.7777777778x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.7777777778x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.7777777778x + x2 = 0 + 2 -0.7777777778x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.7777777778x + x2 = 2 The x term is -0.7777777778x. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778x + 0.1512345679 + x2 = 2 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 2 + 0.1512345679 Combine like terms: 2 + 0.1512345679 = 2.1512345679 0.1512345679 + -0.7777777778x + x2 = 2.1512345679 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 2.1512345679 Calculate the square root of the right side: 1.466708754 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 1.466708754 and -1.466708754.Subproblem 1
x + -0.3888888889 = 1.466708754 Simplifying x + -0.3888888889 = 1.466708754 Reorder the terms: -0.3888888889 + x = 1.466708754 Solving -0.3888888889 + x = 1.466708754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = 1.466708754 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 1.466708754 + 0.3888888889 x = 1.466708754 + 0.3888888889 Combine like terms: 1.466708754 + 0.3888888889 = 1.8555976429 x = 1.8555976429 Simplifying x = 1.8555976429Subproblem 2
x + -0.3888888889 = -1.466708754 Simplifying x + -0.3888888889 = -1.466708754 Reorder the terms: -0.3888888889 + x = -1.466708754 Solving -0.3888888889 + x = -1.466708754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = -1.466708754 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -1.466708754 + 0.3888888889 x = -1.466708754 + 0.3888888889 Combine like terms: -1.466708754 + 0.3888888889 = -1.0778198651 x = -1.0778198651 Simplifying x = -1.0778198651Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8555976429, -1.0778198651}
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