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Simplifying 9x2 + -99x + -100 = 0 Reorder the terms: -100 + -99x + 9x2 = 0 Solving -100 + -99x + 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'. -11.11111111 + -11x + x2 = 0 Move the constant term to the right: Add '11.11111111' to each side of the equation. -11.11111111 + -11x + 11.11111111 + x2 = 0 + 11.11111111 Reorder the terms: -11.11111111 + 11.11111111 + -11x + x2 = 0 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + -11x + x2 = 0 + 11.11111111 -11x + x2 = 0 + 11.11111111 Combine like terms: 0 + 11.11111111 = 11.11111111 -11x + x2 = 11.11111111 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 11.11111111 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 11.11111111 + 30.25 Combine like terms: 11.11111111 + 30.25 = 41.36111111 30.25 + -11x + x2 = 41.36111111 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 41.36111111 Calculate the square root of the right side: 6.43126046 Break this problem into two subproblems by setting (x + -5.5) equal to 6.43126046 and -6.43126046.Subproblem 1
x + -5.5 = 6.43126046 Simplifying x + -5.5 = 6.43126046 Reorder the terms: -5.5 + x = 6.43126046 Solving -5.5 + x = 6.43126046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.43126046 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.43126046 + 5.5 x = 6.43126046 + 5.5 Combine like terms: 6.43126046 + 5.5 = 11.93126046 x = 11.93126046 Simplifying x = 11.93126046Subproblem 2
x + -5.5 = -6.43126046 Simplifying x + -5.5 = -6.43126046 Reorder the terms: -5.5 + x = -6.43126046 Solving -5.5 + x = -6.43126046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.43126046 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.43126046 + 5.5 x = -6.43126046 + 5.5 Combine like terms: -6.43126046 + 5.5 = -0.93126046 x = -0.93126046 Simplifying x = -0.93126046Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.93126046, -0.93126046}
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