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Simplifying c * c + 3c = 55 Multiply c * c c2 + 3c = 55 Reorder the terms: 3c + c2 = 55 Solving 3c + c2 = 55 Solving for variable 'c'. Reorder the terms: -55 + 3c + c2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + 3c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 3c + 55 + c2 = 0 + 55 Reorder the terms: -55 + 55 + 3c + c2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 3c + c2 = 0 + 55 3c + c2 = 0 + 55 Combine like terms: 0 + 55 = 55 3c + c2 = 55 The c term is 3c. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3c + 2.25 + c2 = 55 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 55 + 2.25 Combine like terms: 55 + 2.25 = 57.25 2.25 + 3c + c2 = 57.25 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (c + 1.5) equal to 7.566372975 and -7.566372975.Subproblem 1
c + 1.5 = 7.566372975 Simplifying c + 1.5 = 7.566372975 Reorder the terms: 1.5 + c = 7.566372975 Solving 1.5 + c = 7.566372975 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = 7.566372975 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 7.566372975 + -1.5 c = 7.566372975 + -1.5 Combine like terms: 7.566372975 + -1.5 = 6.066372975 c = 6.066372975 Simplifying c = 6.066372975Subproblem 2
c + 1.5 = -7.566372975 Simplifying c + 1.5 = -7.566372975 Reorder the terms: 1.5 + c = -7.566372975 Solving 1.5 + c = -7.566372975 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = -7.566372975 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -7.566372975 + -1.5 c = -7.566372975 + -1.5 Combine like terms: -7.566372975 + -1.5 = -9.066372975 c = -9.066372975 Simplifying c = -9.066372975Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.066372975, -9.066372975}
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