5c^2+35c+35=0

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Solution for 5c^2+35c+35=0 equation:


Simplifying
5c2 + 35c + 35 = 0

Reorder the terms:
35 + 35c + 5c2 = 0

Solving
35 + 35c + 5c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + 7c + c2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(7 + 7c + c2)' equal to zero and attempt to solve: Simplifying 7 + 7c + c2 = 0 Solving 7 + 7c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 7c + -7 + c2 = 0 + -7 Reorder the terms: 7 + -7 + 7c + c2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7c + c2 = 0 + -7 7c + c2 = 0 + -7 Combine like terms: 0 + -7 = -7 7c + c2 = -7 The c term is 7c. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7c + 12.25 + c2 = -7 + 12.25 Reorder the terms: 12.25 + 7c + c2 = -7 + 12.25 Combine like terms: -7 + 12.25 = 5.25 12.25 + 7c + c2 = 5.25 Factor a perfect square on the left side: (c + 3.5)(c + 3.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (c + 3.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

c + 3.5 = 2.291287847 Simplifying c + 3.5 = 2.291287847 Reorder the terms: 3.5 + c = 2.291287847 Solving 3.5 + c = 2.291287847 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = 2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = 2.291287847 + -3.5 c = 2.291287847 + -3.5 Combine like terms: 2.291287847 + -3.5 = -1.208712153 c = -1.208712153 Simplifying c = -1.208712153

Subproblem 2

c + 3.5 = -2.291287847 Simplifying c + 3.5 = -2.291287847 Reorder the terms: 3.5 + c = -2.291287847 Solving 3.5 + c = -2.291287847 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = -2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = -2.291287847 + -3.5 c = -2.291287847 + -3.5 Combine like terms: -2.291287847 + -3.5 = -5.791287847 c = -5.791287847 Simplifying c = -5.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. c = {-1.208712153, -5.791287847}

Solution

c = {-1.208712153, -5.791287847}

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