Which method do you use to solve 7x^{2}+8x+100?

Nataly Best

Nataly Best

Answered question

2022-01-23

Which method do you use to solve
7x2+8x+100?

Answer & Explanation

Brynn Ortiz

Brynn Ortiz

Beginner2022-01-24Added 12 answers

Step 1
A quadratic equation is simply another way of solving a problem if the solution cannot be factored logically.
First we can start with some quick review:
Let’s say we have the equation
x2+2x3
for example. This equation could be solved logically using the factors of the first and last terms.
To begin, we can state the factors of the first term, x2. Imagine there’s an invisible 1 in front of the x2, therefore the factors are 1, because only 1×1, or 1×1 will multiply to get one. Then we can analyze the third term, -3. The factors of -3 are either 1×3, or 1×3
Now we can check and see if any of the factors can combine in order to get a+2 the middle term (don’t worry about the x’s, those will carry over). Recall
1=1,1 and 3=1, 1,3,3
From our factors we can use a -1 and a 3 to get +2. Therefore,
(x+3)(x1)=0
is our derived factorization. Then plug in the values to make the statement true, -3 or 1 will both result in an answer of 0 and our the possible values for x.
However, when the logical factorization seen above is not possible, we can plug our numbers into the quadratic equation.
ax2+bx+c
is the standard way we view an equation. Using the values from the equation above, a=1, b=2, and c=3
After our a, b, and c values are found we can plug them into the actual quadratic equation.
b±b24ac2a
Note : This equation may look intimidating, but as long as you follow factoring rules, you should have no problem. It’s totally normal to come out with an answer containing square roots.
immablondevl

immablondevl

Beginner2022-01-25Added 11 answers

Step 1
We do not ''solve'' expressions.
Perhaps you want to know how to solve the equation
7x2+8x+100=0
Or perhaps you want to know how to factor the expression
7x2+8x+100
In order to do the second for this expression, we'll have to do the first. That's because this expression is irreducible using real, rational coefficients.
Solve:
7x2+8x+100=0
Spend a little time factoring, but not too much, because we know we can always solve by the quadratic formula.
x=b±b2ac2a
For the equation we're working on:
x=(8)±(8)24(7)(100)2(7)
so
x=8±64280014=8±273614
=8±1219i14=47±6197i
Note
Simplifying 2736 is not trivial.
2736 is divisible by 9 (the digits add up to 18, which is divisible by 9)
2736=9×304
304 is divisible by 4 (half or 304 is still even, so we can divide again)
2736=9×4×76 (half of 76 is 38, still even)
2736=9×4×4×19
So
2736=9×4×4×19=3×2×2×19=1219
Now that we know the zeros of
7x2+8x+100
are z1 and z2, we can factor the quadratic as (xz1)(xz2), so:
7x2+8x+100=(x(47+6197i))(x(476197i))

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