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Simplifying 8c * 8c + 26c + -7 = 0 Reorder the terms for easier multiplication: 8 * 8c * c + 26c + -7 = 0 Multiply 8 * 8 64c * c + 26c + -7 = 0 Multiply c * c 64c2 + 26c + -7 = 0 Reorder the terms: -7 + 26c + 64c2 = 0 Solving -7 + 26c + 64c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.109375 + 0.40625c + c2 = 0 Move the constant term to the right: Add '0.109375' to each side of the equation. -0.109375 + 0.40625c + 0.109375 + c2 = 0 + 0.109375 Reorder the terms: -0.109375 + 0.109375 + 0.40625c + c2 = 0 + 0.109375 Combine like terms: -0.109375 + 0.109375 = 0.000000 0.000000 + 0.40625c + c2 = 0 + 0.109375 0.40625c + c2 = 0 + 0.109375 Combine like terms: 0 + 0.109375 = 0.109375 0.40625c + c2 = 0.109375 The c term is 0.40625c. Take half its coefficient (0.203125). Square it (0.04125976563) and add it to both sides. Add '0.04125976563' to each side of the equation. 0.40625c + 0.04125976563 + c2 = 0.109375 + 0.04125976563 Reorder the terms: 0.04125976563 + 0.40625c + c2 = 0.109375 + 0.04125976563 Combine like terms: 0.109375 + 0.04125976563 = 0.15063476563 0.04125976563 + 0.40625c + c2 = 0.15063476563 Factor a perfect square on the left side: (c + 0.203125)(c + 0.203125) = 0.15063476563 Calculate the square root of the right side: 0.388116948 Break this problem into two subproblems by setting (c + 0.203125) equal to 0.388116948 and -0.388116948.Subproblem 1
c + 0.203125 = 0.388116948 Simplifying c + 0.203125 = 0.388116948 Reorder the terms: 0.203125 + c = 0.388116948 Solving 0.203125 + c = 0.388116948 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.203125' to each side of the equation. 0.203125 + -0.203125 + c = 0.388116948 + -0.203125 Combine like terms: 0.203125 + -0.203125 = 0.000000 0.000000 + c = 0.388116948 + -0.203125 c = 0.388116948 + -0.203125 Combine like terms: 0.388116948 + -0.203125 = 0.184991948 c = 0.184991948 Simplifying c = 0.184991948Subproblem 2
c + 0.203125 = -0.388116948 Simplifying c + 0.203125 = -0.388116948 Reorder the terms: 0.203125 + c = -0.388116948 Solving 0.203125 + c = -0.388116948 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.203125' to each side of the equation. 0.203125 + -0.203125 + c = -0.388116948 + -0.203125 Combine like terms: 0.203125 + -0.203125 = 0.000000 0.000000 + c = -0.388116948 + -0.203125 c = -0.388116948 + -0.203125 Combine like terms: -0.388116948 + -0.203125 = -0.591241948 c = -0.591241948 Simplifying c = -0.591241948Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.184991948, -0.591241948}
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