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Simplifying 10c2 + -11c + -3 = 0 Reorder the terms: -3 + -11c + 10c2 = 0 Solving -3 + -11c + 10c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -1.1c + c2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -1.1c + 0.3 + c2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.1c + c2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.1c + c2 = 0 + 0.3 -1.1c + c2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -1.1c + c2 = 0.3 The c term is -1.1c. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1c + 0.3025 + c2 = 0.3 + 0.3025 Reorder the terms: 0.3025 + -1.1c + c2 = 0.3 + 0.3025 Combine like terms: 0.3 + 0.3025 = 0.6025 0.3025 + -1.1c + c2 = 0.6025 Factor a perfect square on the left side: (c + -0.55)(c + -0.55) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (c + -0.55) equal to 0.776208735 and -0.776208735.Subproblem 1
c + -0.55 = 0.776208735 Simplifying c + -0.55 = 0.776208735 Reorder the terms: -0.55 + c = 0.776208735 Solving -0.55 + c = 0.776208735 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + c = 0.776208735 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + c = 0.776208735 + 0.55 c = 0.776208735 + 0.55 Combine like terms: 0.776208735 + 0.55 = 1.326208735 c = 1.326208735 Simplifying c = 1.326208735Subproblem 2
c + -0.55 = -0.776208735 Simplifying c + -0.55 = -0.776208735 Reorder the terms: -0.55 + c = -0.776208735 Solving -0.55 + c = -0.776208735 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + c = -0.776208735 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + c = -0.776208735 + 0.55 c = -0.776208735 + 0.55 Combine like terms: -0.776208735 + 0.55 = -0.226208735 c = -0.226208735 Simplifying c = -0.226208735Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.326208735, -0.226208735}
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