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Simplifying 56X2 + -15X + -15 = 0 Reorder the terms: -15 + -15X + 56X2 = 0 Solving -15 + -15X + 56X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -0.2678571429 + -0.2678571429X + X2 = 0 Move the constant term to the right: Add '0.2678571429' to each side of the equation. -0.2678571429 + -0.2678571429X + 0.2678571429 + X2 = 0 + 0.2678571429 Reorder the terms: -0.2678571429 + 0.2678571429 + -0.2678571429X + X2 = 0 + 0.2678571429 Combine like terms: -0.2678571429 + 0.2678571429 = 0.0000000000 0.0000000000 + -0.2678571429X + X2 = 0 + 0.2678571429 -0.2678571429X + X2 = 0 + 0.2678571429 Combine like terms: 0 + 0.2678571429 = 0.2678571429 -0.2678571429X + X2 = 0.2678571429 The X term is -0.2678571429X. Take half its coefficient (-0.1339285715). Square it (0.01793686226) and add it to both sides. Add '0.01793686226' to each side of the equation. -0.2678571429X + 0.01793686226 + X2 = 0.2678571429 + 0.01793686226 Reorder the terms: 0.01793686226 + -0.2678571429X + X2 = 0.2678571429 + 0.01793686226 Combine like terms: 0.2678571429 + 0.01793686226 = 0.28579400516 0.01793686226 + -0.2678571429X + X2 = 0.28579400516 Factor a perfect square on the left side: (X + -0.1339285715)(X + -0.1339285715) = 0.28579400516 Calculate the square root of the right side: 0.534597049 Break this problem into two subproblems by setting (X + -0.1339285715) equal to 0.534597049 and -0.534597049.Subproblem 1
X + -0.1339285715 = 0.534597049 Simplifying X + -0.1339285715 = 0.534597049 Reorder the terms: -0.1339285715 + X = 0.534597049 Solving -0.1339285715 + X = 0.534597049 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.1339285715' to each side of the equation. -0.1339285715 + 0.1339285715 + X = 0.534597049 + 0.1339285715 Combine like terms: -0.1339285715 + 0.1339285715 = 0.0000000000 0.0000000000 + X = 0.534597049 + 0.1339285715 X = 0.534597049 + 0.1339285715 Combine like terms: 0.534597049 + 0.1339285715 = 0.6685256205 X = 0.6685256205 Simplifying X = 0.6685256205Subproblem 2
X + -0.1339285715 = -0.534597049 Simplifying X + -0.1339285715 = -0.534597049 Reorder the terms: -0.1339285715 + X = -0.534597049 Solving -0.1339285715 + X = -0.534597049 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.1339285715' to each side of the equation. -0.1339285715 + 0.1339285715 + X = -0.534597049 + 0.1339285715 Combine like terms: -0.1339285715 + 0.1339285715 = 0.0000000000 0.0000000000 + X = -0.534597049 + 0.1339285715 X = -0.534597049 + 0.1339285715 Combine like terms: -0.534597049 + 0.1339285715 = -0.4006684775 X = -0.4006684775 Simplifying X = -0.4006684775Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.6685256205, -0.4006684775}
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