C^2+8c-16= - Solution

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c^2+8c-16=

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Equation:

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Solution for c^2+8c-16= equation:

Simplifying c2 + 8c + -16 = 0 Reorder the terms: -16 + 8c + c2 = 0 Solving -16 + 8c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 8c + 16 + c2 = 0 + 16 Reorder the terms: -16 + 16 + 8c + c2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 8c + c2 = 0 + 16 8c + c2 = 0 + 16 Combine like terms: 0 + 16 = 16 8c + c2 = 16 The c term is 8c. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8c + 16 + c2 = 16 + 16 Reorder the terms: 16 + 8c + c2 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + 8c + c2 = 32 Factor a perfect square on the left side: (c + 4)(c + 4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (c + 4) equal to 5.656854249 and -5.656854249.

Subproblem 1

c + 4 = 5.656854249 Simplifying c + 4 = 5.656854249 Reorder the terms: 4 + c = 5.656854249 Solving 4 + c = 5.656854249 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + c = 5.656854249 + -4 c = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 c = 1.656854249 Simplifying c = 1.656854249

Subproblem 2

c + 4 = -5.656854249 Simplifying c + 4 = -5.656854249 Reorder the terms: 4 + c = -5.656854249 Solving 4 + c = -5.656854249 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + c = -5.656854249 + -4 c = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 c = -9.656854249 Simplifying c = -9.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. c = {1.656854249, -9.656854249}

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