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Simplifying c2 + -15c + -96 = 0 Reorder the terms: -96 + -15c + c2 = 0 Solving -96 + -15c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -15c + 96 + c2 = 0 + 96 Reorder the terms: -96 + 96 + -15c + c2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -15c + c2 = 0 + 96 -15c + c2 = 0 + 96 Combine like terms: 0 + 96 = 96 -15c + c2 = 96 The c term is -15c. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15c + 56.25 + c2 = 96 + 56.25 Reorder the terms: 56.25 + -15c + c2 = 96 + 56.25 Combine like terms: 96 + 56.25 = 152.25 56.25 + -15c + c2 = 152.25 Factor a perfect square on the left side: (c + -7.5)(c + -7.5) = 152.25 Calculate the square root of the right side: 12.338962679 Break this problem into two subproblems by setting (c + -7.5) equal to 12.338962679 and -12.338962679.Subproblem 1
c + -7.5 = 12.338962679 Simplifying c + -7.5 = 12.338962679 Reorder the terms: -7.5 + c = 12.338962679 Solving -7.5 + c = 12.338962679 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + c = 12.338962679 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + c = 12.338962679 + 7.5 c = 12.338962679 + 7.5 Combine like terms: 12.338962679 + 7.5 = 19.838962679 c = 19.838962679 Simplifying c = 19.838962679Subproblem 2
c + -7.5 = -12.338962679 Simplifying c + -7.5 = -12.338962679 Reorder the terms: -7.5 + c = -12.338962679 Solving -7.5 + c = -12.338962679 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + c = -12.338962679 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + c = -12.338962679 + 7.5 c = -12.338962679 + 7.5 Combine like terms: -12.338962679 + 7.5 = -4.838962679 c = -4.838962679 Simplifying c = -4.838962679Solution
The solution to the problem is based on the solutions from the subproblems. c = {19.838962679, -4.838962679}
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