Find the x and the measure of each angle
1 answer:
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Answer:
Equation:
Solve for n: n = 112
Step-by-step explanation:
To first set up the equation, you need to look at the verbal description and translate into numbers and operations:
'three fourths a number' =
'plus 8' = + 8
'is' =
'20 less' = - 20
'the number' = n
Put the expressions together:
'three fourths a number plus 8':
'20 less than the number': n - 20
Set them equal to each other and solve:
Add 20 to both sides:
Subtract from both sides:
Multiply both sides by :
Solve for n: n = 112
This is a quadratic equation, i.e. an equation involving a polynomial of degree 2. To solve them, you must rearrange them first, so that all terms are on the same side, so we get
i.e. now we're looking for the roots of the polynomial. To find them, we can use the following formula:
where is a compact way to indicate both solutions
and
, while
are the coefficients of the quadratic equation, i.e. we consider the polynomial
.
So, in your case, we have
Plug those values into the formula to get
So, the two solutions are