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Simplifying 4.9x2 + 335x + -636.5 = 0 Reorder the terms: -636.5 + 335x + 4.9x2 = 0 Solving -636.5 + 335x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -129.8979592 + 68.36734694x + x2 = 0 Move the constant term to the right: Add '129.8979592' to each side of the equation. -129.8979592 + 68.36734694x + 129.8979592 + x2 = 0 + 129.8979592 Reorder the terms: -129.8979592 + 129.8979592 + 68.36734694x + x2 = 0 + 129.8979592 Combine like terms: -129.8979592 + 129.8979592 = 0.0000000 0.0000000 + 68.36734694x + x2 = 0 + 129.8979592 68.36734694x + x2 = 0 + 129.8979592 Combine like terms: 0 + 129.8979592 = 129.8979592 68.36734694x + x2 = 129.8979592 The x term is 68.36734694x. Take half its coefficient (34.18367347). Square it (1168.523532) and add it to both sides. Add '1168.523532' to each side of the equation. 68.36734694x + 1168.523532 + x2 = 129.8979592 + 1168.523532 Reorder the terms: 1168.523532 + 68.36734694x + x2 = 129.8979592 + 1168.523532 Combine like terms: 129.8979592 + 1168.523532 = 1298.4214912 1168.523532 + 68.36734694x + x2 = 1298.4214912 Factor a perfect square on the left side: (x + 34.18367347)(x + 34.18367347) = 1298.4214912 Calculate the square root of the right side: 36.033616127 Break this problem into two subproblems by setting (x + 34.18367347) equal to 36.033616127 and -36.033616127.Subproblem 1
x + 34.18367347 = 36.033616127 Simplifying x + 34.18367347 = 36.033616127 Reorder the terms: 34.18367347 + x = 36.033616127 Solving 34.18367347 + x = 36.033616127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.18367347' to each side of the equation. 34.18367347 + -34.18367347 + x = 36.033616127 + -34.18367347 Combine like terms: 34.18367347 + -34.18367347 = 0.00000000 0.00000000 + x = 36.033616127 + -34.18367347 x = 36.033616127 + -34.18367347 Combine like terms: 36.033616127 + -34.18367347 = 1.849942657 x = 1.849942657 Simplifying x = 1.849942657Subproblem 2
x + 34.18367347 = -36.033616127 Simplifying x + 34.18367347 = -36.033616127 Reorder the terms: 34.18367347 + x = -36.033616127 Solving 34.18367347 + x = -36.033616127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.18367347' to each side of the equation. 34.18367347 + -34.18367347 + x = -36.033616127 + -34.18367347 Combine like terms: 34.18367347 + -34.18367347 = 0.00000000 0.00000000 + x = -36.033616127 + -34.18367347 x = -36.033616127 + -34.18367347 Combine like terms: -36.033616127 + -34.18367347 = -70.217289597 x = -70.217289597 Simplifying x = -70.217289597Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.849942657, -70.217289597}
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