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Simplifying 9x2 + -99x + -100 = 10 Reorder the terms: -100 + -99x + 9x2 = 10 Solving -100 + -99x + 9x2 = 10 Solving for variable 'x'. Reorder the terms: -100 + -10 + -99x + 9x2 = 10 + -10 Combine like terms: -100 + -10 = -110 -110 + -99x + 9x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -110 + -99x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -12.22222222 + -11x + x2 = 0 Move the constant term to the right: Add '12.22222222' to each side of the equation. -12.22222222 + -11x + 12.22222222 + x2 = 0 + 12.22222222 Reorder the terms: -12.22222222 + 12.22222222 + -11x + x2 = 0 + 12.22222222 Combine like terms: -12.22222222 + 12.22222222 = 0.00000000 0.00000000 + -11x + x2 = 0 + 12.22222222 -11x + x2 = 0 + 12.22222222 Combine like terms: 0 + 12.22222222 = 12.22222222 -11x + x2 = 12.22222222 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 = 12.22222222 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 12.22222222 + 30.25 Combine like terms: 12.22222222 + 30.25 = 42.47222222 30.25 + -11x + x2 = 42.47222222 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 42.47222222 Calculate the square root of the right side: 6.517071599 Break this problem into two subproblems by setting (x + -5.5) equal to 6.517071599 and -6.517071599.Subproblem 1
x + -5.5 = 6.517071599 Simplifying x + -5.5 = 6.517071599 Reorder the terms: -5.5 + x = 6.517071599 Solving -5.5 + x = 6.517071599 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 = 6.517071599 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.517071599 + 5.5 x = 6.517071599 + 5.5 Combine like terms: 6.517071599 + 5.5 = 12.017071599 x = 12.017071599 Simplifying x = 12.017071599Subproblem 2
x + -5.5 = -6.517071599 Simplifying x + -5.5 = -6.517071599 Reorder the terms: -5.5 + x = -6.517071599 Solving -5.5 + x = -6.517071599 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 = -6.517071599 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.517071599 + 5.5 x = -6.517071599 + 5.5 Combine like terms: -6.517071599 + 5.5 = -1.017071599 x = -1.017071599 Simplifying x = -1.017071599Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.017071599, -1.017071599}
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