SOLUTION: Thank you for staying! Take your time and please help me <3 Solve the equation by using square roots. 1.) 2x^2+6=14 2.) (x-1)^2+3=12 Solve the equation by comp

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Thank you for staying! Take your time and please help me <3 Solve the equation by using square roots. 1.) 2x^2+6=14 2.) (x-1)^2+3=12 Solve the equation by comp      Log On


   

Question 1028738: Thank you for staying! Take your time and please help me <3

Solve the equation by using square roots.

1.) 2x^2+6=14

2.) (x-1)^2+3=12

Solve the equation by completing the square. Round to the nearest tenth, if necessary.

3.) x^2+6x=7

4.) x^2-4x=10

Write the function in vertex form by completing the square.

5.) y=x^2+2x+1

6.) y=-x^2-8x-15

Again, I just wanted to thank you guys so much!


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Knowing how to change to vertex form means you will know how to both solve by taking/using square root and how to Complete the Square.

See how to complete the square here: How to solve using Completing The Square



highlight_green%28y=x%5E2%2B2x%2B1%29
Already a perfect square so no need to complete the square. Just factorize the perfect square trinomial:
y=%28x%2B1%29%5E2
which you could also show as highlight%28y=1%28x%2B1%29%5E2%2B0%29.

highlight_green%28y=-x%5E2-8x-15%29
y=-1%28x%5E2%2B8x%2B15%29
The term to complete the square INSIDE the parenthesized expression is 16.
y=-1%28x%5E2%2B8x%2B16-15-16%29
y=-1%28%28x%2B4%29%5E2-31%29
highlight%28y=-1%28x%2B4%29%5E2%2B31%29