Question

WILL ADD BRANLIEST

A= 7x^2-3x+10
B= -4x^2+6x-4

What is A - B

Answer 1

Answer:

$A-B=11x^2-9x+14$

Step-by-step explanation:

• These are our given values.

$A= 7x^2-3x+10\\B= -4x^2+6x-4$

• Use substitution so we only have to solve for 1 unknown, $x$.

$A-B=(7x^2-3x+10)-(-4x^2+6x-4)$

• Distribute the negative sign into what was substituted in for $B$. Remember that every value in the parentheses is affected by the negative, and that a negative times a negative equals a positive.
• ($- * - = +$).

$A-B=7x^2-3x+10+4x^2-6x+4$

• After distributing, we only have addition and subtraction remaining, so we can get rid of the parentheses.
• Now, let's add like terms.

$A-B=7x^2-3x+10+4x^2-6x+4\\A-B=7x^2+4x^2-3x-6x+10+4\\A-B=11x^2-9x+14$

Our final answer is:

$A-B=11x^2-9x+14$

If you wanted to solve for $x$ to see if you could get an actual number as an answer:

• Our previously final answer is a standard-form quadratic equation. Standard-form will always be formatted like so:
• $f(x)=ax^2+bx+c$ where $a$, $b$, and $c$ are 3 different, constant values.

$A-B=11x^2-9x+14$

$a=11\\b=-9\\c=14$

• At this point, we will need to use the quadratic formula to find $x$. The equation is shown below:

• $x=\frac{-b+-\sqrt{b^2-4ac}}{2a}$

• NOTE 1: the values in this formula correspond to the standard form equation shown above.

• NOTE 2: please treat the $+-$ symbols as a ± symbol because this site does not let me type ± when doing an equation.
• NOTE 3: Factoring does not work in this case, so I'm resorting to the quadratic equation, but if you can, avoid using this equation as it is tedious and time consuming.

$x=\frac{-b+-\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-9)+-\sqrt{(-9)^2-4(11)(14)}}{2(11)}$

• Now, let's solve for $x$.

$x=\frac{-(-9)+-\sqrt{(-9)^2-4(11)(14)}}{2(11)}\\x=\frac{9+-\sqrt{81-616}}{22}\\x=\frac{9+-\sqrt{-535}}{22}$

• No solution because you cannot square root a negative and get a real number as your answer.
• I could go into the use of $i$ or $\sqrt{-1}$, but even this would not result in clean math and would just be a pain to solve.