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Simplifying 19.5x2 + -349x + 1156 = 0 Reorder the terms: 1156 + -349x + 19.5x2 = 0 Solving 1156 + -349x + 19.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19.5 the coefficient of the squared term: Divide each side by '19.5'. 59.28205128 + -17.8974359x + x2 = 0 Move the constant term to the right: Add '-59.28205128' to each side of the equation. 59.28205128 + -17.8974359x + -59.28205128 + x2 = 0 + -59.28205128 Reorder the terms: 59.28205128 + -59.28205128 + -17.8974359x + x2 = 0 + -59.28205128 Combine like terms: 59.28205128 + -59.28205128 = 0.00000000 0.00000000 + -17.8974359x + x2 = 0 + -59.28205128 -17.8974359x + x2 = 0 + -59.28205128 Combine like terms: 0 + -59.28205128 = -59.28205128 -17.8974359x + x2 = -59.28205128 The x term is -17.8974359x. Take half its coefficient (-8.94871795). Square it (80.07955295) and add it to both sides. Add '80.07955295' to each side of the equation. -17.8974359x + 80.07955295 + x2 = -59.28205128 + 80.07955295 Reorder the terms: 80.07955295 + -17.8974359x + x2 = -59.28205128 + 80.07955295 Combine like terms: -59.28205128 + 80.07955295 = 20.79750167 80.07955295 + -17.8974359x + x2 = 20.79750167 Factor a perfect square on the left side: (x + -8.94871795)(x + -8.94871795) = 20.79750167 Calculate the square root of the right side: 4.560427795 Break this problem into two subproblems by setting (x + -8.94871795) equal to 4.560427795 and -4.560427795.Subproblem 1
x + -8.94871795 = 4.560427795 Simplifying x + -8.94871795 = 4.560427795 Reorder the terms: -8.94871795 + x = 4.560427795 Solving -8.94871795 + x = 4.560427795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.94871795' to each side of the equation. -8.94871795 + 8.94871795 + x = 4.560427795 + 8.94871795 Combine like terms: -8.94871795 + 8.94871795 = 0.00000000 0.00000000 + x = 4.560427795 + 8.94871795 x = 4.560427795 + 8.94871795 Combine like terms: 4.560427795 + 8.94871795 = 13.509145745 x = 13.509145745 Simplifying x = 13.509145745Subproblem 2
x + -8.94871795 = -4.560427795 Simplifying x + -8.94871795 = -4.560427795 Reorder the terms: -8.94871795 + x = -4.560427795 Solving -8.94871795 + x = -4.560427795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.94871795' to each side of the equation. -8.94871795 + 8.94871795 + x = -4.560427795 + 8.94871795 Combine like terms: -8.94871795 + 8.94871795 = 0.00000000 0.00000000 + x = -4.560427795 + 8.94871795 x = -4.560427795 + 8.94871795 Combine like terms: -4.560427795 + 8.94871795 = 4.388290155 x = 4.388290155 Simplifying x = 4.388290155Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.509145745, 4.388290155}
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