How to Solve By Completing the Square (NancyPi)

MIT grad shows the easiest way to complete the square to solve a quadratic equation. To skip ahead: 1) for a quadratic that STARTS WITH X^2, skip to time 1:42. 2) For a quadratic that STARTS WITH 2X^2, 3X^2, etc., skip to time 6:46. 3) For NEGATIVE leading term like -X^2, skip to 13:34. 4) If there's NO X TERM (ex. 3x^2 - 121 = 0), then you cannot complete the square and can solve directly - skip to 16:30. Nancy formerly of MathBFF explains the steps.

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How to complete the square when solving quadratic equations:

Completing the square means re-arranging the quadratic equation into the neat, "perfect square" form (x + number)^2 equals another number, or (x - number)^2 equals another number. The point of doing this is so that you can solve by just square-rooting both sides of the equation.

If your quadratic equation starts with...

1) just X^2 (for ex: x^2 + 6x - 7 = 0), move constant to right, add (6/2)^2 to both sides, write left side as perfect square, and square root both sides to solve. Remember you get PLUS and MINUS solutions when you square root the constant side.

2) 2X^2 or 3X^2 or 4X^2 etc. (for ex: 2x^2 - 10x - 3 = 0), move constant to right side, DIVIDE EVERY TERM by leading coefficient 2 on left and right side, add (5/2)^2 to both sides, write left side as perfect square and square root both sides to solve.

3) -X^2 or any negative coefficient (for ex: -x^2 - 6x + 7 = 0), move constant to right side, DIVIDE EVERY TERM by -1 on left and right side. (NOTE: if you had -2x^2 in your equation, you would divide every term by -2 on left and right side). Then add (6/2)^2 to both sides, write left side as perfect square and square root both sides to solve.

If you don't have an X term in equation, (for ex: 3x^2 - 121 = 0), then you cannot complete the square. Just move the constant to the right, divide both sides by 3, and square root both sides to solve. Remember plus and minus solutions on the right.

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