How do you solve #x^2 + 4x = 0# by completing the square?

Answer 1

Isaiah Anthony

#x=0 or x=-4#

#x^2+4x =0 or (x+2)^2-4=0 or (x+2)^2=4 or (x+2)=+-2 or x=-2+-2:. x=0 or x=-4#[Ans]

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Answer 2

Eva Abramson

To solve the equation x^2 + 4x = 0 by completing the square, follow these steps:

Move the constant term to the other side of the equation: x^2 + 4x = 0 x^2 + 4x - 0 = 0
Identify and halve the coefficient of the linear term (4x), then square it: (4/2)^2 = 4
Add the squared value obtained in step 2 to both sides of the equation: x^2 + 4x + 4 = 4
Rewrite the left side of the equation as a perfect square trinomial: (x + 2)^2 = 4
Take the square root of both sides and solve for x: x + 2 = ±√4 x + 2 = ±2 x = -2 ± 2
Solve for x: x = -2 + 2 = 0 x = -2 - 2 = -4

So, the solutions to the equation x^2 + 4x = 0 are x = 0 and x = -4.

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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.