Question

How To Solve Quadratic Equations With A Very Large Constant And Has Not Given With A Coefficient Of x²?
Relevant Example: x²+400 x - 960000 = 0.

(It takes lot of time to factor 960000 and find two numbers that when subtracted from one from the other we get +400 and when multiplied the product becomes 960000).

Please Help Me Out...

Answer 1

Answer:

X= -1200  , 800

Step-by-step explanation:

You can use the following methods to solve the quadratic equations with x².

Using the Quadratic Formula:

The formula is:

              $x=\frac {-b±\sqrt{b^2-4ac} }{2a}$

where,the quadratic equation should be in the following form:

    $ax^{2} +bx+c=0$

note : b^2-ac should be greater than 0.

Completing the square method:

This is another method where the quadratic equation should be in form of:

x²+px+q=0 .

• First you need to rewrite the equation such that the constant term on the right hand side of the equation should become:

i.e. x²+ px = -q.

$x^{2} +400x = 960000$

• Now, add $(\frac{p}{2} )$ to the both sides of the equation to form the following:

$(x+\frac{p}{2} )^{2} =(\frac{p}{2} )^{2} -q$

i.e=$x^{2} +(\frac{400}{2})^{2} =960000+(\frac{400}{2})^{2}$

• Lastly,take the square root on both sides of the equation to further solve for the x.

$\sqrt{(x+200)^{2} } =\sqrt{1000000}$

then,

x= (±sqrt{1000000} ) - 200

x= (sqrt{1000000}) - 200    or

      x= (- sqrt{1000000}) - 200

x= -1200 , 800