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Simplifying 3x * 3x + 7x + -6 = 0 Reorder the terms for easier multiplication: 3 * 3x * x + 7x + -6 = 0 Multiply 3 * 3 9x * x + 7x + -6 = 0 Multiply x * x 9x2 + 7x + -6 = 0 Reorder the terms: -6 + 7x + 9x2 = 0 Solving -6 + 7x + 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'. -0.6666666667 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.7777777778x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.7777777778x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + 0.6666666667 0.7777777778x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.7777777778x + x2 = 0.6666666667 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 = 0.6666666667 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 0.6666666667 + 0.1512345679 Combine like terms: 0.6666666667 + 0.1512345679 = 0.8179012346 0.1512345679 + 0.7777777778x + x2 = 0.8179012346 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 0.8179012346 Calculate the square root of the right side: 0.904378922 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 0.904378922 and -0.904378922.Subproblem 1
x + 0.3888888889 = 0.904378922 Simplifying x + 0.3888888889 = 0.904378922 Reorder the terms: 0.3888888889 + x = 0.904378922 Solving 0.3888888889 + x = 0.904378922 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 = 0.904378922 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 0.904378922 + -0.3888888889 x = 0.904378922 + -0.3888888889 Combine like terms: 0.904378922 + -0.3888888889 = 0.5154900331 x = 0.5154900331 Simplifying x = 0.5154900331Subproblem 2
x + 0.3888888889 = -0.904378922 Simplifying x + 0.3888888889 = -0.904378922 Reorder the terms: 0.3888888889 + x = -0.904378922 Solving 0.3888888889 + x = -0.904378922 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 = -0.904378922 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -0.904378922 + -0.3888888889 x = -0.904378922 + -0.3888888889 Combine like terms: -0.904378922 + -0.3888888889 = -1.2932678109 x = -1.2932678109 Simplifying x = -1.2932678109Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5154900331, -1.2932678109}
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