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Simplifying 9x2 + -8x + -71 = 0 Reorder the terms: -71 + -8x + 9x2 = 0 Solving -71 + -8x + 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'. -7.888888889 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '7.888888889' to each side of the equation. -7.888888889 + -0.8888888889x + 7.888888889 + x2 = 0 + 7.888888889 Reorder the terms: -7.888888889 + 7.888888889 + -0.8888888889x + x2 = 0 + 7.888888889 Combine like terms: -7.888888889 + 7.888888889 = 0.000000000 0.000000000 + -0.8888888889x + x2 = 0 + 7.888888889 -0.8888888889x + x2 = 0 + 7.888888889 Combine like terms: 0 + 7.888888889 = 7.888888889 -0.8888888889x + x2 = 7.888888889 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 7.888888889 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 7.888888889 + 0.1975308642 Combine like terms: 7.888888889 + 0.1975308642 = 8.0864197532 0.1975308642 + -0.8888888889x + x2 = 8.0864197532 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 8.0864197532 Calculate the square root of the right side: 2.843663087 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 2.843663087 and -2.843663087.Subproblem 1
x + -0.4444444445 = 2.843663087 Simplifying x + -0.4444444445 = 2.843663087 Reorder the terms: -0.4444444445 + x = 2.843663087 Solving -0.4444444445 + x = 2.843663087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 2.843663087 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 2.843663087 + 0.4444444445 x = 2.843663087 + 0.4444444445 Combine like terms: 2.843663087 + 0.4444444445 = 3.2881075315 x = 3.2881075315 Simplifying x = 3.2881075315Subproblem 2
x + -0.4444444445 = -2.843663087 Simplifying x + -0.4444444445 = -2.843663087 Reorder the terms: -0.4444444445 + x = -2.843663087 Solving -0.4444444445 + x = -2.843663087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -2.843663087 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -2.843663087 + 0.4444444445 x = -2.843663087 + 0.4444444445 Combine like terms: -2.843663087 + 0.4444444445 = -2.3992186425 x = -2.3992186425 Simplifying x = -2.3992186425Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2881075315, -2.3992186425}
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