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Simplifying 5c2 + 5c + -36 = 0 Reorder the terms: -36 + 5c + 5c2 = 0 Solving -36 + 5c + 5c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + c + c2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + c + 7.2 + c2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + c + c2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + c + c2 = 0 + 7.2 c + c2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 c + c2 = 7.2 The c term is c. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + c2 = 7.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + c2 = 7.2 + 0.25 Combine like terms: 7.2 + 0.25 = 7.45 1.25 + c2 = 7.45 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 7.45 Calculate the square root of the right side: 2.729468813 Break this problem into two subproblems by setting (c + 0.5) equal to 2.729468813 and -2.729468813.Subproblem 1
c + 0.5 = 2.729468813 Simplifying c + 0.5 = 2.729468813 Reorder the terms: 0.5 + c = 2.729468813 Solving 0.5 + c = 2.729468813 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = 2.729468813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 2.729468813 + -0.5 c = 2.729468813 + -0.5 Combine like terms: 2.729468813 + -0.5 = 2.229468813 c = 2.229468813 Simplifying c = 2.229468813Subproblem 2
c + 0.5 = -2.729468813 Simplifying c + 0.5 = -2.729468813 Reorder the terms: 0.5 + c = -2.729468813 Solving 0.5 + c = -2.729468813 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = -2.729468813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -2.729468813 + -0.5 c = -2.729468813 + -0.5 Combine like terms: -2.729468813 + -0.5 = -3.229468813 c = -3.229468813 Simplifying c = -3.229468813Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.229468813, -3.229468813}
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