Explanation:
Consider ...
x/a = b/c . . . . . find x
Multiplying by the denominator under x gives ...
x = ab/c . . . . the value of the unknown.
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In the case where the unknown is in the denominator, you can invert the ratios and solve as above:
a/x = c/b . . . . . note that x is in the denominator
x/a = b/c . . . . . equivalent equation, solve as above
<span>Simplifying
3a2 + -2a + -1 = 0
Reorder the terms:
-1 + -2a + 3a2 = 0
Solving
-1 + -2a + 3a2 = 0
Solving for variable 'a'.
Factor a trinomial.
(-1 + -3a)(1 + -1a) = 0
Subproblem 1Set the factor '(-1 + -3a)' equal to zero and attempt to solve:
Simplifying
-1 + -3a = 0
Solving
-1 + -3a = 0
Move all terms containing a to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + -3a = 0 + 1
Combine like terms: -1 + 1 = 0
0 + -3a = 0 + 1
-3a = 0 + 1
Combine like terms: 0 + 1 = 1
-3a = 1
Divide each side by '-3'.
a = -0.3333333333
Simplifying
a = -0.3333333333
Subproblem 2Set the factor '(1 + -1a)' equal to zero and attempt to solve:
Simplifying
1 + -1a = 0
Solving
1 + -1a = 0
Move all terms containing a to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1a = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1
Combine like terms: 0 + -1 = -1
-1a = -1
Divide each side by '-1'.
a = 1
Simplifying
a = 1Solutiona = {-0.3333333333, 1}</span>
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