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Simplifying -9x2 + 7x + 8 = 0 Reorder the terms: 8 + 7x + -9x2 = 0 Solving 8 + 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'. -0.8888888889 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.7777777778x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.7777777778x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.7777777778x + x2 = 0 + 0.8888888889 -0.7777777778x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.7777777778x + x2 = 0.8888888889 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 = 0.8888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 0.8888888889 + 0.1512345679 Combine like terms: 0.8888888889 + 0.1512345679 = 1.0401234568 0.1512345679 + -0.7777777778x + x2 = 1.0401234568 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 1.0401234568 Calculate the square root of the right side: 1.019864431 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 1.019864431 and -1.019864431.Subproblem 1
x + -0.3888888889 = 1.019864431 Simplifying x + -0.3888888889 = 1.019864431 Reorder the terms: -0.3888888889 + x = 1.019864431 Solving -0.3888888889 + x = 1.019864431 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 = 1.019864431 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 1.019864431 + 0.3888888889 x = 1.019864431 + 0.3888888889 Combine like terms: 1.019864431 + 0.3888888889 = 1.4087533199 x = 1.4087533199 Simplifying x = 1.4087533199Subproblem 2
x + -0.3888888889 = -1.019864431 Simplifying x + -0.3888888889 = -1.019864431 Reorder the terms: -0.3888888889 + x = -1.019864431 Solving -0.3888888889 + x = -1.019864431 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 = -1.019864431 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -1.019864431 + 0.3888888889 x = -1.019864431 + 0.3888888889 Combine like terms: -1.019864431 + 0.3888888889 = -0.6309755421 x = -0.6309755421 Simplifying x = -0.6309755421Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4087533199, -0.6309755421}
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