x^2-400x+40000=0-এর সমাধান করুন

$$x ^ { 2 } - 400 x + 40000 = 0$$

Solve for x

$$x=200$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}-400x+40000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -400 for b, and 40000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-400\right)±\sqrt{\left(-400\right)^{2}-4\times 40000}}{2}$$

Square -400.

$$x=\frac{-\left(-400\right)±\sqrt{160000-4\times 40000}}{2}$$

Multiply -4 times 40000.

$$x=\frac{-\left(-400\right)±\sqrt{160000-160000}}{2}$$

Add 160000 to -160000.

$$x=\frac{-\left(-400\right)±\sqrt{0}}{2}$$

Take the square root of 0.

$$x=-\frac{-400}{2}$$

The opposite of -400 is 400.

$$x=\frac{400}{2}$$

Divide 400 by 2.

$$x=200$$

Steps for Completing the Square

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}-400x+40000=0$$

Factor x^{2}-400x+40000. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-200\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-200\right)^{2}}=\sqrt{0}$$

Simplify.

$$x-200=0 x-200=0$$

Add 200 to both sides of the equation.

$$x=200 x=200$$

The equation is now solved. Solutions are the same.

$$x=200$$