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How do you solve #3x^2 - 10 = 2x# by completing the square?

Answer 1

Genesis Allen

#3x^2 - 10 = 2x rArr 3x^2 - 2x = 10#

#x^2 - (2x)/3 + color(red)((1/3)^2) = 10/3 + color(red)((1/3)^2)# #(x - 1/3)^2 = 31/9#

#x - 1/3 = +-sqrt31/3#

# x = sqrt31/3 + 1/3 " or " x = -sqrt31/3 + 1/3#

#x = 2.189 or x = -1.523#

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Answer 2

Savannah Anderson

To solve the equation 3x^2 - 10 = 2x by completing the square, follow these steps:

Move all terms to one side to set the equation to zero: 3x^2 - 2x - 10 = 0.
Add (b/2)^2 to both sides, where b is the coefficient of x: (2/2)^2 = 1. Add 1 to both sides of the equation.
Rewrite the equation in squared form: 3(x^2 - (2/3)x) = 11.
Factor the perfect square trinomial inside the parentheses: 3(x - 1/3)^2 = 11.
Divide both sides by the coefficient of the squared term to isolate the squared term: (x - 1/3)^2 = 11/3.
Take the square root of both sides: x - 1/3 = ±√(11/3).
Add 1/3 to both sides to solve for x: x = 1/3 ± √(11/3).

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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.