How do you solve #x^2 = x + 2 #?

Answer 1

Kennedy Adams

#x = 2#

#x^2 = x + 2#

#x^2 - x= 2#

#(x * x )-x = 2#

#(x*x)-x = x * (x - 1)#

#x *(x-1) = 2#

#(2-1)x = 2#

#1x = 2#

#1 = 2/x#

#x = 2#

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Answer 2

Abigail Allen

To solve the equation (x^2 = x + 2), you first rearrange it to form a quadratic equation in standard form, set it equal to zero, then solve for (x) using factoring, completing the square, or the quadratic formula. Here's the step-by-step process:

Subtract (x) and 2 from both sides to get (x^2 - x - 2 = 0).
Factor the quadratic expression: ((x - 2)(x + 1) = 0).
Set each factor equal to zero and solve for (x):
- (x - 2 = 0) gives (x = 2).
- (x + 1 = 0) gives (x = -1).

So, the solutions to the equation (x^2 = x + 2) are (x = 2) and (x = -1).

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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.