2c^2+8c-9=0

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Solution for 2c^2+8c-9=0 equation:


Simplifying
2c2 + 8c + -9 = 0

Reorder the terms:
-9 + 8c + 2c2 = 0

Solving
-9 + 8c + 2c2 = 0

Solving for variable 'c'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-4.5 + 4c + c2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 4c + 4.5 + c2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 4c + c2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 4c + c2 = 0 + 4.5
4c + c2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
4c + c2 = 4.5

The c term is 4c.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4c + 4 + c2 = 4.5 + 4

Reorder the terms:
4 + 4c + c2 = 4.5 + 4

Combine like terms: 4.5 + 4 = 8.5
4 + 4c + c2 = 8.5

Factor a perfect square on the left side:
(c + 2)(c + 2) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(c + 2) equal to 2.915475947 and -2.915475947.

Subproblem 1

c + 2 = 2.915475947 Simplifying c + 2 = 2.915475947 Reorder the terms: 2 + c = 2.915475947 Solving 2 + c = 2.915475947 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + c = 2.915475947 + -2 c = 2.915475947 + -2 Combine like terms: 2.915475947 + -2 = 0.915475947 c = 0.915475947 Simplifying c = 0.915475947

Subproblem 2

c + 2 = -2.915475947 Simplifying c + 2 = -2.915475947 Reorder the terms: 2 + c = -2.915475947 Solving 2 + c = -2.915475947 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = -2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + c = -2.915475947 + -2 c = -2.915475947 + -2 Combine like terms: -2.915475947 + -2 = -4.915475947 c = -4.915475947 Simplifying c = -4.915475947

Solution

The solution to the problem is based on the solutions from the subproblems. c = {0.915475947, -4.915475947}

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