Question

How do you solve \[{{x}^{2}}-8x=20\]?

Answer 1

Hint: From the question, we have been given that to solve \[{{x}^{2}}-8x=20\].We can solve the given equation by transforming the given equation into quadratic equation. Then, by the method of factorization or by using the quadratic formula, we can solve the given equation.

Complete step-by-step answer:
From the question, we have been given that \[{{x}^{2}}-8x=20\]
Now to transform the given equation into a quadratic equation shift \[20\] from the right hand side of the equation to the left hand side of the equation.
By shifting \[20\] from right hand side of the equation to the left hand side of the equation, we get \[{{x}^{2}}-8x-20=0\]
Now, by using the factorization process, we have to solve the obtained quadratic equation.
As a process, first of all, we have to write \[20\] into a product of two numbers, so that the sum of two numbers will be equal to the coefficient of \[x\].
\[20\]can be written as a product of \[2\text{ and -10}\].
Now, the obtained quadratic equation can be written as,
\[{{x}^{2}}-8x-20=0\]
\[\Rightarrow {{x}^{2}}+2x-10x-20=0\]
Now by taking the terms common out from the above equation, we get the below equation,
\[x\left( x+2 \right)-10\left( x+2 \right)=0\]
\[\Rightarrow \left( x-10 \right)\left( x+2 \right)=0\]
By using the zero property, we get \[x-10=0\text{ and x+2=0}\]
Therefore \[x=10\] and \[x=-2\] are the factors for the obtained quadratic equation.
Hence, the given equation is solved by using the factorization process.

Note: We should be well known about the process of factorization. Also, we should be very careful while writing the constant into the product of the two numbers, because the whole sum is dependent on that constant. Also, we should be careful while doing the calculation. Also, we should be careful while converting the given equation into the quadratic equation. This question can also be answered by using the formulae to solve any quadratic equation $a{{x}^{2}}+bx+c=0$ given as $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ . For this sum it will be \[{{x}^{2}}-8x=20\Rightarrow {{x}^{2}}-8x-20=0\] given as $x=\dfrac{-\left( -8 \right)\pm \sqrt{{{\left( -8 \right)}^{2}}-4\left( 1 \right)\left( -20 \right)}}{2\left( 1 \right)}\Rightarrow x=\dfrac{8\pm \sqrt{64+80}}{2}\Rightarrow x=4\pm 6\Rightarrow x=10,-2$ .