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Simplifying 9.9x2 + 21x + -10 = 0 Reorder the terms: -10 + 21x + 9.9x2 = 0 Solving -10 + 21x + 9.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.9 the coefficient of the squared term: Divide each side by '9.9'. -1.01010101 + 2.121212121x + x2 = 0 Move the constant term to the right: Add '1.01010101' to each side of the equation. -1.01010101 + 2.121212121x + 1.01010101 + x2 = 0 + 1.01010101 Reorder the terms: -1.01010101 + 1.01010101 + 2.121212121x + x2 = 0 + 1.01010101 Combine like terms: -1.01010101 + 1.01010101 = 0.00000000 0.00000000 + 2.121212121x + x2 = 0 + 1.01010101 2.121212121x + x2 = 0 + 1.01010101 Combine like terms: 0 + 1.01010101 = 1.01010101 2.121212121x + x2 = 1.01010101 The x term is 2.121212121x. Take half its coefficient (1.060606061). Square it (1.124885217) and add it to both sides. Add '1.124885217' to each side of the equation. 2.121212121x + 1.124885217 + x2 = 1.01010101 + 1.124885217 Reorder the terms: 1.124885217 + 2.121212121x + x2 = 1.01010101 + 1.124885217 Combine like terms: 1.01010101 + 1.124885217 = 2.134986227 1.124885217 + 2.121212121x + x2 = 2.134986227 Factor a perfect square on the left side: (x + 1.060606061)(x + 1.060606061) = 2.134986227 Calculate the square root of the right side: 1.461159207 Break this problem into two subproblems by setting (x + 1.060606061) equal to 1.461159207 and -1.461159207.Subproblem 1
x + 1.060606061 = 1.461159207 Simplifying x + 1.060606061 = 1.461159207 Reorder the terms: 1.060606061 + x = 1.461159207 Solving 1.060606061 + x = 1.461159207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.060606061' to each side of the equation. 1.060606061 + -1.060606061 + x = 1.461159207 + -1.060606061 Combine like terms: 1.060606061 + -1.060606061 = 0.000000000 0.000000000 + x = 1.461159207 + -1.060606061 x = 1.461159207 + -1.060606061 Combine like terms: 1.461159207 + -1.060606061 = 0.400553146 x = 0.400553146 Simplifying x = 0.400553146Subproblem 2
x + 1.060606061 = -1.461159207 Simplifying x + 1.060606061 = -1.461159207 Reorder the terms: 1.060606061 + x = -1.461159207 Solving 1.060606061 + x = -1.461159207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.060606061' to each side of the equation. 1.060606061 + -1.060606061 + x = -1.461159207 + -1.060606061 Combine like terms: 1.060606061 + -1.060606061 = 0.000000000 0.000000000 + x = -1.461159207 + -1.060606061 x = -1.461159207 + -1.060606061 Combine like terms: -1.461159207 + -1.060606061 = -2.521765268 x = -2.521765268 Simplifying x = -2.521765268Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.400553146, -2.521765268}
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