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Simplifying -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 = 1.2932678109 x = 1.2932678109 Simplifying x = 1.2932678109Subproblem 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 = -0.5154900331 x = -0.5154900331 Simplifying x = -0.5154900331Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2932678109, -0.5154900331}
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