q^2=-7q+18

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Solution for q^2=-7q+18 equation:


Simplifying
q2 = -7q + 18

Reorder the terms:
q2 = 18 + -7q

Solving
q2 = 18 + -7q

Solving for variable 'q'.

Reorder the terms:
-18 + 7q + q2 = 18 + -7q + -18 + 7q

Reorder the terms:
-18 + 7q + q2 = 18 + -18 + -7q + 7q

Combine like terms: 18 + -18 = 0
-18 + 7q + q2 = 0 + -7q + 7q
-18 + 7q + q2 = -7q + 7q

Combine like terms: -7q + 7q = 0
-18 + 7q + q2 = 0

Factor a trinomial.
(-9 + -1q)(2 + -1q) = 0

Subproblem 1

Set the factor '(-9 + -1q)' equal to zero and attempt to solve: Simplifying -9 + -1q = 0 Solving -9 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1q = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1q = 0 + 9 -1q = 0 + 9 Combine like terms: 0 + 9 = 9 -1q = 9 Divide each side by '-1'. q = -9 Simplifying q = -9

Subproblem 2

Set the factor '(2 + -1q)' equal to zero and attempt to solve: Simplifying 2 + -1q = 0 Solving 2 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1q = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1q = 0 + -2 -1q = 0 + -2 Combine like terms: 0 + -2 = -2 -1q = -2 Divide each side by '-1'. q = 2 Simplifying q = 2

Solution

q = {-9, 2}

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