(c-3)(c-3)=49

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Solution for (c-3)(c-3)=49 equation:


Simplifying
(c + -3)(c + -3) = 49

Reorder the terms:
(-3 + c)(c + -3) = 49

Reorder the terms:
(-3 + c)(-3 + c) = 49

Multiply (-3 + c) * (-3 + c)
(-3(-3 + c) + c(-3 + c)) = 49
((-3 * -3 + c * -3) + c(-3 + c)) = 49
((9 + -3c) + c(-3 + c)) = 49
(9 + -3c + (-3 * c + c * c)) = 49
(9 + -3c + (-3c + c2)) = 49

Combine like terms: -3c + -3c = -6c
(9 + -6c + c2) = 49

Solving
9 + -6c + c2 = 49

Solving for variable 'c'.

Reorder the terms:
9 + -49 + -6c + c2 = 49 + -49

Combine like terms: 9 + -49 = -40
-40 + -6c + c2 = 49 + -49

Combine like terms: 49 + -49 = 0
-40 + -6c + c2 = 0

Factor a trinomial.
(-4 + -1c)(10 + -1c) = 0

Subproblem 1

Set the factor '(-4 + -1c)' equal to zero and attempt to solve: Simplifying -4 + -1c = 0 Solving -4 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1c = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1c = 0 + 4 -1c = 0 + 4 Combine like terms: 0 + 4 = 4 -1c = 4 Divide each side by '-1'. c = -4 Simplifying c = -4

Subproblem 2

Set the factor '(10 + -1c)' equal to zero and attempt to solve: Simplifying 10 + -1c = 0 Solving 10 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1c = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1c = 0 + -10 -1c = 0 + -10 Combine like terms: 0 + -10 = -10 -1c = -10 Divide each side by '-1'. c = 10 Simplifying c = 10

Solution

c = {-4, 10}

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