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Simplifying 0 = (-4.9x2) + 14x + 38 Reorder the terms: 0 = 38 + 14x + (-4.9x2) Solving 0 = 38 + 14x + (-4.9x2) Solving for variable 'x'. Combine like terms: 0 + -38 = -38 -38 + -14x + (4.9x2) = 38 + 14x + (-4.9x2) + -38 + -14x + (4.9x2) Reorder the terms: -38 + -14x + (4.9x2) = 38 + -38 + 14x + -14x + (-4.9x2) + (4.9x2) Combine like terms: 38 + -38 = 0 -38 + -14x + (4.9x2) = 0 + 14x + -14x + (-4.9x2) + (4.9x2) -38 + -14x + (4.9x2) = 14x + -14x + (-4.9x2) + (4.9x2) Combine like terms: 14x + -14x = 0 -38 + -14x + (4.9x2) = 0 + (-4.9x2) + (4.9x2) -38 + -14x + (4.9x2) = (-4.9x2) + (4.9x2) Combine like terms: (-4.9x2) + (4.9x2) = 0.0 -38 + -14x + (4.9x2) = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -7.755102041 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '7.755102041' to each side of the equation. -7.755102041 + -2.857142857x + 7.755102041 + x2 = 0 + 7.755102041 Reorder the terms: -7.755102041 + 7.755102041 + -2.857142857x + x2 = 0 + 7.755102041 Combine like terms: -7.755102041 + 7.755102041 = 0.000000000 0.000000000 + -2.857142857x + x2 = 0 + 7.755102041 -2.857142857x + x2 = 0 + 7.755102041 Combine like terms: 0 + 7.755102041 = 7.755102041 -2.857142857x + x2 = 7.755102041 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 7.755102041 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 7.755102041 + 2.040816328 Combine like terms: 7.755102041 + 2.040816328 = 9.795918369 2.040816328 + -2.857142857x + x2 = 9.795918369 Factor a perfect square on the left side: ((x) + -1.428571429)((x) + -1.428571429) = 9.795918369 Calculate the square root of the right side: 3.129843186 Break this problem into two subproblems by setting ((x) + -1.428571429) equal to 3.129843186 and -3.129843186.Subproblem 1
(x) + -1.428571429 = 3.129843186 Simplifying (x) + -1.428571429 = 3.129843186 x + -1.428571429 = 3.129843186 Reorder the terms: -1.428571429 + x = 3.129843186 Solving -1.428571429 + x = 3.129843186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 3.129843186 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 3.129843186 + 1.428571429 x = 3.129843186 + 1.428571429 Combine like terms: 3.129843186 + 1.428571429 = 4.558414615 x = 4.558414615 Simplifying x = 4.558414615Subproblem 2
(x) + -1.428571429 = -3.129843186 Simplifying (x) + -1.428571429 = -3.129843186 x + -1.428571429 = -3.129843186 Reorder the terms: -1.428571429 + x = -3.129843186 Solving -1.428571429 + x = -3.129843186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -3.129843186 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -3.129843186 + 1.428571429 x = -3.129843186 + 1.428571429 Combine like terms: -3.129843186 + 1.428571429 = -1.701271757 x = -1.701271757 Simplifying x = -1.701271757Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.558414615, -1.701271757}
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