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Simplifying 9x2 + -80x + 50 = 0 Reorder the terms: 50 + -80x + 9x2 = 0 Solving 50 + -80x + 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'. 5.555555556 + -8.888888889x + x2 = 0 Move the constant term to the right: Add '-5.555555556' to each side of the equation. 5.555555556 + -8.888888889x + -5.555555556 + x2 = 0 + -5.555555556 Reorder the terms: 5.555555556 + -5.555555556 + -8.888888889x + x2 = 0 + -5.555555556 Combine like terms: 5.555555556 + -5.555555556 = 0.000000000 0.000000000 + -8.888888889x + x2 = 0 + -5.555555556 -8.888888889x + x2 = 0 + -5.555555556 Combine like terms: 0 + -5.555555556 = -5.555555556 -8.888888889x + x2 = -5.555555556 The x term is -8.888888889x. Take half its coefficient (-4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. -8.888888889x + 19.75308642 + x2 = -5.555555556 + 19.75308642 Reorder the terms: 19.75308642 + -8.888888889x + x2 = -5.555555556 + 19.75308642 Combine like terms: -5.555555556 + 19.75308642 = 14.197530864 19.75308642 + -8.888888889x + x2 = 14.197530864 Factor a perfect square on the left side: (x + -4.444444445)(x + -4.444444445) = 14.197530864 Calculate the square root of the right side: 3.767961102 Break this problem into two subproblems by setting (x + -4.444444445) equal to 3.767961102 and -3.767961102.Subproblem 1
x + -4.444444445 = 3.767961102 Simplifying x + -4.444444445 = 3.767961102 Reorder the terms: -4.444444445 + x = 3.767961102 Solving -4.444444445 + x = 3.767961102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = 3.767961102 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = 3.767961102 + 4.444444445 x = 3.767961102 + 4.444444445 Combine like terms: 3.767961102 + 4.444444445 = 8.212405547 x = 8.212405547 Simplifying x = 8.212405547Subproblem 2
x + -4.444444445 = -3.767961102 Simplifying x + -4.444444445 = -3.767961102 Reorder the terms: -4.444444445 + x = -3.767961102 Solving -4.444444445 + x = -3.767961102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = -3.767961102 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = -3.767961102 + 4.444444445 x = -3.767961102 + 4.444444445 Combine like terms: -3.767961102 + 4.444444445 = 0.676483343 x = 0.676483343 Simplifying x = 0.676483343Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.212405547, 0.676483343}
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