Solving Quadratic Equations: Completing the Squares
Why “quadratic?” Is 4 its lucky number? Or does it just spend a lot of time at the gym?
|Mathematics and Statistics Assessment||Quadratic and Other Polynomial Expressions, and Functions|
|Quadratic Equations||Quadratic Equations|
has to solve this problem:
Two-x-squared plus five-x minus 42 equals zero. [Man stood in a hard hat next to a blu print sheet]
Okay to solve first, add forty-two to both sides to get...
…two-x-squared plus eight-x equals 42.
Divide every term by two so that the number before the x-squared is 1.
…x-squared plus four-x equals twenty-one.
It's time to complete the square. [Woman holding the equation on a sheet waiting expectantly]
We want to add a number to the left side such that it becomes a perfect square.
We can find this number by taking the coefficient of the x-term, dividing it by 2, and squaring
In this case, our coefficient of the x term is 4.
4 divided by 2 equals 2.
Two-squared equals 4.
We've found the number that completes the square. [The answer is highlighted]
Whatever we do to one side, we have to do to the other.
So we add 4 to both sides, which gets us x squared plus 4x plus 4 equals 21 plus 4.
Now we can factor the left side of the equation. [The left side is highlighted]
X-squared plus four-x plus four can be simplified to x plus 2 in parentheses squared.
To simplify the right-hand side, we add 21 and 4 to get 25. [The right hand side is highlighted]
All that's left is to take the square root of both sides. [Both sides have a square root sign drawn over them]
Don't forget that the square root can be positive or negative. [Finger appears with piece of knotted string attached]
We're left with x plus 2 equals plus-or-minus the square-root of 25, or just 5.
Subtract two from both sides...
and we get two answers.
x equals either negative 2 plus 5..
…or negative 2 minus 5.. which gives us 3 and negative 7.
And there you have it! [Man in the hard hat points to the answer]
The equation for the square is complete.
And Pocket Square is complete as well. [The QuadSquad car reverses away]