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Simplifying 1.2454x2 + 34.9x + -19.6 = 0 Reorder the terms: -19.6 + 34.9x + 1.2454x2 = 0 Solving -19.6 + 34.9x + 1.2454x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.2454 the coefficient of the squared term: Divide each side by '1.2454'. -15.73791553 + 28.0231251x + x2 = 0 Move the constant term to the right: Add '15.73791553' to each side of the equation. -15.73791553 + 28.0231251x + 15.73791553 + x2 = 0 + 15.73791553 Reorder the terms: -15.73791553 + 15.73791553 + 28.0231251x + x2 = 0 + 15.73791553 Combine like terms: -15.73791553 + 15.73791553 = 0.00000000 0.00000000 + 28.0231251x + x2 = 0 + 15.73791553 28.0231251x + x2 = 0 + 15.73791553 Combine like terms: 0 + 15.73791553 = 15.73791553 28.0231251x + x2 = 15.73791553 The x term is 28.0231251x. Take half its coefficient (14.01156255). Square it (196.3238851) and add it to both sides. Add '196.3238851' to each side of the equation. 28.0231251x + 196.3238851 + x2 = 15.73791553 + 196.3238851 Reorder the terms: 196.3238851 + 28.0231251x + x2 = 15.73791553 + 196.3238851 Combine like terms: 15.73791553 + 196.3238851 = 212.06180063 196.3238851 + 28.0231251x + x2 = 212.06180063 Factor a perfect square on the left side: (x + 14.01156255)(x + 14.01156255) = 212.06180063 Calculate the square root of the right side: 14.562341866 Break this problem into two subproblems by setting (x + 14.01156255) equal to 14.562341866 and -14.562341866.Subproblem 1
x + 14.01156255 = 14.562341866 Simplifying x + 14.01156255 = 14.562341866 Reorder the terms: 14.01156255 + x = 14.562341866 Solving 14.01156255 + x = 14.562341866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.01156255' to each side of the equation. 14.01156255 + -14.01156255 + x = 14.562341866 + -14.01156255 Combine like terms: 14.01156255 + -14.01156255 = 0.00000000 0.00000000 + x = 14.562341866 + -14.01156255 x = 14.562341866 + -14.01156255 Combine like terms: 14.562341866 + -14.01156255 = 0.550779316 x = 0.550779316 Simplifying x = 0.550779316Subproblem 2
x + 14.01156255 = -14.562341866 Simplifying x + 14.01156255 = -14.562341866 Reorder the terms: 14.01156255 + x = -14.562341866 Solving 14.01156255 + x = -14.562341866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.01156255' to each side of the equation. 14.01156255 + -14.01156255 + x = -14.562341866 + -14.01156255 Combine like terms: 14.01156255 + -14.01156255 = 0.00000000 0.00000000 + x = -14.562341866 + -14.01156255 x = -14.562341866 + -14.01156255 Combine like terms: -14.562341866 + -14.01156255 = -28.573904416 x = -28.573904416 Simplifying x = -28.573904416Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.550779316, -28.573904416}
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