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Simplifying 5c2 + -5c + -25 = 0 Reorder the terms: -25 + -5c + 5c2 = 0 Solving -25 + -5c + 5c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + -1c + c2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -1c + c2)' equal to zero and attempt to solve: Simplifying -5 + -1c + c2 = 0 Solving -5 + -1c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -1c + 5 + c2 = 0 + 5 Reorder the terms: -5 + 5 + -1c + c2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1c + c2 = 0 + 5 -1c + c2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1c + c2 = 5 The c term is -1c. 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. -1c + 0.25 + c2 = 5 + 0.25 Reorder the terms: 0.25 + -1c + c2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1c + c2 = 5.25 Factor a perfect square on the left side: (c + -0.5)(c + -0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (c + -0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
c + -0.5 = 2.291287847 Simplifying c + -0.5 = 2.291287847 Reorder the terms: -0.5 + c = 2.291287847 Solving -0.5 + c = 2.291287847 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 = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = 2.291287847 + 0.5 c = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 c = 2.791287847 Simplifying c = 2.791287847Subproblem 2
c + -0.5 = -2.291287847 Simplifying c + -0.5 = -2.291287847 Reorder the terms: -0.5 + c = -2.291287847 Solving -0.5 + c = -2.291287847 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 = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = -2.291287847 + 0.5 c = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 c = -1.791287847 Simplifying c = -1.791287847Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.791287847, -1.791287847}Solution
c = {2.791287847, -1.791287847}
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