401cbe6204
Fixed typo "quadratic eduation" to "quadratic equation".
Some grammar seemed off so that was changed as well.
😁
2.3 KiB
2.3 KiB
title
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| Completing the Square |
Completing the Square
The completing the square method is one of the many methods for solving a quadratic equation. It involves changing the form of the equation so that the left side becomes a perfect square.
A quadratic equation generally takes the form: ax2 + bx + c = 0. To solve the above, follow these steps:
- Move the constant value to the Right Hand Side of the equation so it becomes:
ax2 + bx = -c
- Make the coefficient of x2 equal to 1 by dividing both sides of the equation by a so that we now have:
x2 + (b/a)x = -(c/a)
- Next, add the square of half of the coefficient of the x-term to both sides of the equation:
x2 + (b/a)x + (b/2a)2 = (b/2a)2 - (c/a)
- Completing the square on the Left Hand Side and simplifying the Right Hand Side of the above equation, we have:
(x + b/2a)2 = (b2/4a2) - (c/a)
- Further simplifying the Right Hand Side,
(x + b/2a)2 = (b2 - 4ac) ÷ 4a2
- Finding the square root of both sides of the equation,
x + b/2a = ±((b2 - 4ac)½ ÷ 2a)
- By making x the subject of our formula, we are able to solve for its value completely:
x = (-b ± (b2 - 4ac)½) ÷ 2a