Completing the Square
Posted by Professor Cram in Equations and Inequalities
Completing the Square
Building on the concept of the Perfect Square Trinomial, the technique of Completing the Square can be used to solve a quadratic equation. This Formula Solver! Series program will walk you through the steps.
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Get More Help!
Click one of these links to get more help from another Cramlet in this same chapter:
- Algebra Quiz of Equality and Inequality
- Bottomless Worksheet of Simple Linear Inequalities
- Bottomless Worksheet of Simple Linear Equations
- Bottomless Worksheet of Quadratic Equations
- Bottomless Worksheet of Completing the Square
- My Equality and Inequality Flashcards
- Solving Simple Linear Inequalities
- Solving Simple Linear Equations
- Solving Quadratic Equations
- Properties of Inequalities
- Completing the Square
please show some examples
Millie,
Did you try the Formula Solver! above? Click “Begin” and “Next” through each step. Use your own values for the variables. Endless examples are possible.
A lot of these examples have answers printed as whole numbers when the answers i have a not whole. have the decimals been rounded out whenever they appear in the equation or only for the answer? i know my answers are correct having gone through the working meticulously.
When I put decimals in for some of the variables to complete the square, I get decimal answers back using the “Solver!” above. I don’t know what Chloe is talking about.
put some example problems sir:D
what if the equation has a minus sign. ex:-5x+60x-145=0
should i subtract on both sides or add.
I’m having trouble finding the second answer from the example? How can I get it? Thanks
Roberto, if you click “Next” a few times you’ll get the final answer which looks something like:
x = {2, -3}
The numbers in the curly brackets — in this case, 2 and -3 — are the two answers that satisfy the equation.
I’m having trouble jumping from the last step to the answer here. Can you explain how to break down the x^-8x=16=25 to (x-4)^=25? I can’t seem to figure out out the reverse the process for me, I can take the answer and make it into the longer equation, but for some reason I can’t figure in my head how to do it the other way. Thanks!
Hi Alison. The step you’re struggling with is factoring, which we cover in another Cramlet on Factoring Trinomials. The left side of the equation is factored (if you multiply out the square you’ll get the previous left side of the equation as a result) while the right side is just combining 9+16.
I hope that helps.
Hi, i am having trouble figuring out where the 16 is comming from?
not where its comming from but why is the 8x staying in the equation when it was divided and squared to make the 16?