q^2=4q+77

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Solution for q^2=4q+77 equation:


Simplifying
q2 = 4q + 77

Reorder the terms:
q2 = 77 + 4q

Solving
q2 = 77 + 4q

Solving for variable 'q'.

Reorder the terms:
-77 + -4q + q2 = 77 + 4q + -77 + -4q

Reorder the terms:
-77 + -4q + q2 = 77 + -77 + 4q + -4q

Combine like terms: 77 + -77 = 0
-77 + -4q + q2 = 0 + 4q + -4q
-77 + -4q + q2 = 4q + -4q

Combine like terms: 4q + -4q = 0
-77 + -4q + q2 = 0

Factor a trinomial.
(-7 + -1q)(11 + -1q) = 0

Subproblem 1

Set the factor '(-7 + -1q)' equal to zero and attempt to solve: Simplifying -7 + -1q = 0 Solving -7 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1q = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1q = 0 + 7 -1q = 0 + 7 Combine like terms: 0 + 7 = 7 -1q = 7 Divide each side by '-1'. q = -7 Simplifying q = -7

Subproblem 2

Set the factor '(11 + -1q)' equal to zero and attempt to solve: Simplifying 11 + -1q = 0 Solving 11 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1q = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1q = 0 + -11 -1q = 0 + -11 Combine like terms: 0 + -11 = -11 -1q = -11 Divide each side by '-1'. q = 11 Simplifying q = 11

Solution

q = {-7, 11}

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