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Simplifying 4.9x2 + 38x + -625 = 0 Reorder the terms: -625 + 38x + 4.9x2 = 0 Solving -625 + 38x + 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'. -127.5510204 + 7.755102041x + x2 = 0 Move the constant term to the right: Add '127.5510204' to each side of the equation. -127.5510204 + 7.755102041x + 127.5510204 + x2 = 0 + 127.5510204 Reorder the terms: -127.5510204 + 127.5510204 + 7.755102041x + x2 = 0 + 127.5510204 Combine like terms: -127.5510204 + 127.5510204 = 0.0000000 0.0000000 + 7.755102041x + x2 = 0 + 127.5510204 7.755102041x + x2 = 0 + 127.5510204 Combine like terms: 0 + 127.5510204 = 127.5510204 7.755102041x + x2 = 127.5510204 The x term is 7.755102041x. Take half its coefficient (3.877551021). Square it (15.03540192) and add it to both sides. Add '15.03540192' to each side of the equation. 7.755102041x + 15.03540192 + x2 = 127.5510204 + 15.03540192 Reorder the terms: 15.03540192 + 7.755102041x + x2 = 127.5510204 + 15.03540192 Combine like terms: 127.5510204 + 15.03540192 = 142.58642232 15.03540192 + 7.755102041x + x2 = 142.58642232 Factor a perfect square on the left side: (x + 3.877551021)(x + 3.877551021) = 142.58642232 Calculate the square root of the right side: 11.94095567 Break this problem into two subproblems by setting (x + 3.877551021) equal to 11.94095567 and -11.94095567.Subproblem 1
x + 3.877551021 = 11.94095567 Simplifying x + 3.877551021 = 11.94095567 Reorder the terms: 3.877551021 + x = 11.94095567 Solving 3.877551021 + x = 11.94095567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.877551021' to each side of the equation. 3.877551021 + -3.877551021 + x = 11.94095567 + -3.877551021 Combine like terms: 3.877551021 + -3.877551021 = 0.000000000 0.000000000 + x = 11.94095567 + -3.877551021 x = 11.94095567 + -3.877551021 Combine like terms: 11.94095567 + -3.877551021 = 8.063404649 x = 8.063404649 Simplifying x = 8.063404649Subproblem 2
x + 3.877551021 = -11.94095567 Simplifying x + 3.877551021 = -11.94095567 Reorder the terms: 3.877551021 + x = -11.94095567 Solving 3.877551021 + x = -11.94095567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.877551021' to each side of the equation. 3.877551021 + -3.877551021 + x = -11.94095567 + -3.877551021 Combine like terms: 3.877551021 + -3.877551021 = 0.000000000 0.000000000 + x = -11.94095567 + -3.877551021 x = -11.94095567 + -3.877551021 Combine like terms: -11.94095567 + -3.877551021 = -15.818506691 x = -15.818506691 Simplifying x = -15.818506691Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.063404649, -15.818506691}
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