Question

How do you combine $\left( 17{{x}^{2}}+7x-14 \right)-\left( -6{{x}^{2}}-5x-18 \right)$ ?

Answer 1

Hint: Here in this question we have been asked to combine the given expression $\left( 17{{x}^{2}}+7x-14 \right)-\left( -6{{x}^{2}}-5x-18 \right)$ . For combining the expression we will add similar terms in the expression and make it in simplified and reduced form.

Complete step by step solution:
Now considering from the question we have been asked to combine the given expression $\left( 17{{x}^{2}}+7x-14 \right)-\left( -6{{x}^{2}}-5x-18 \right)$ .
For combining the expression we will add similar terms in the expression and make it in simplified and reduced form.
Now we will remove the brackets and simply write this as $ 17{{x}^{2}}+7x-14+6{{x}^{2}}+5x+18$ .
Then we will add $17{{x}^{2}}$ and $6{{x}^{2}}$ and then replace the result after removing the two terms in the expression. This process is the process of simple basic arithmetic addition of two different numbers. After performing it we will have $ 23{{x}^{2}}+7x-14+5x+18$ .
Similarly now we will add $7x$ and $5x$ and then replace the result after removing the two terms in the expression. This process is the process of simple basic arithmetic addition of two different numbers. After performing it we will have $ 23{{x}^{2}}+12x-14+18$ .
Similarly now we will add $-14$ and $18$ and then replace the result after removing the two terms in the expression. This process is the process of simple basic arithmetic addition of two different numbers. After performing it we will have $ 23{{x}^{2}}+12x+4$ .
Therefore we can conclude that the simplified form of the given expression $\left( 17{{x}^{2}}+7x-14 \right)-\left( -6{{x}^{2}}-5x-18 \right)$ is $23{{x}^{2}}+12x+4$ .

Note: In questions of this type we need to perform simple basic arithmetic operations like addition, subtraction, multiplication and division between similar terms to simplify and reduce the given expression. These questions take very less time and very few calculation mistakes are possible in this type. Similarly we can combine or simplify or reduce any expression. We can further simplify this and find the value of $x$ by using the quadratic formula for finding roots of any quadratic expression in the form of $a{{x}^{2}}+bx+c$is given as
$\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ . For this expression the values of $x$ will be $\dfrac{-12\pm \sqrt{{{12}^{2}}-4\left( 23 \right)\left( 4 \right)}}{2\left( 23 \right)}=\dfrac{-12\pm \sqrt{144-368}}{2\left( 23 \right)}\Rightarrow \dfrac{-12\pm \sqrt{-224}}{2\left( 23 \right)}=\dfrac{-12\pm i14.9}{2\left( 23 \right)}$ . This has imaginary and conjugate roots.