How do you solve #x^2 + 6x = 3# using completing the square?

Answer 1

To complete the square you add #9# to both sides.

Method : you halve the #x#-coefficient (#6#) to get #3#, and the square of that (#9#) is needed to complete the square.
#->x^2+6x+9=3+9#
#->(x+3)^2=12->x+3=+-sqrt12=+-2sqrt3#
#->x_(1,2)=-3+-2sqrt3#
(remember #+-# means two solutions, one with + and one with -)
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To solve ( x^2 + 6x = 3 ) using completing the square:

  1. Move the constant term to the other side: ( x^2 + 6x - 3 = 0 ).
  2. Add and subtract ((\frac{6}{2})^2 = 9) within the expression: ( x^2 + 6x + 9 - 9 - 3 = 0 ).
  3. Rewrite the expression as a perfect square trinomial and simplify: ( (x + 3)^2 - 12 = 0 ).
  4. Add 12 to both sides: ( (x + 3)^2 = 12 ).
  5. Take the square root of both sides: ( x + 3 = \pm \sqrt{12} ).
  6. Simplify the square root: ( x + 3 = \pm 2\sqrt{3} ).
  7. Subtract 3 from both sides: ( x = -3 \pm 2\sqrt{3} ).

So, the solutions to the equation ( x^2 + 6x = 3 ) using completing the square are ( x = -3 + 2\sqrt{3} ) and ( x = -3 - 2\sqrt{3} ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7