Question

Solve the equation $x^2+10x=200$

a) by completing the square

b) using the Quadratic Formula

c) Which method do you prefer? Why?

Short answer

$x=-20,10.$

Step-by-step solution

Step 1. Given 

$\mathrm{Given}\mathrm{equation}\mathrm{is},x^2+10x=200.$

Step 1. Part ( a ) 

$$\begin{gathered} \mathrm{Using}\mathrm{completing}\mathrm{the}\mathrm{square}\mathrm{method}, \\ {x}^2+10x-200=0 \\ {x}^2+2\left(5\right)\left(x\right)+{\left(5\right)}^2-{\left(5\right)}^2-200=0 \\ {(x+5)}^2-{\left(15\right)}^2=0 \\ \mathrm{Using}\mathrm{identity},a^2-b^2=(a-b)(a+b) \\ (x+5-15)(x+5+15)=0 \\ x=-20,x=10. \end{gathered}$$

Step 3. Part ( b ) 

$$\begin{gathered} U\sin gquadraticformula, \\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}, \\ {x}^2+10x-200=0 \\ Now, \\ x=\frac{-10\pm \sqrt{{\left(10\right)}^2-4\left(1\right)(-200)}}{2} \\ x=\frac{-10\pm \sqrt{900}}{2} \\ x=\frac{-10+30}{2}=10,x=\frac{-10-30}{2}=-20 \end{gathered}$$

Step 4. Part ( c ) 

Quadratic formula – is the method that is used most often for solving a quadratic equation. If you are using factoring or the quadratic formula, make sure that the equation is in standard form.

Step 5. Check part 

Verifying that the roots of given equation is -20 and 10 .

$$\begin{gathered} {\left(-20\right)}^2+10\left(-20\right)=400-200=200=R.H.S \\ {\left(10\right)}^2+10\left(10\right)=100+100=200=R.H.S \end{gathered}$$