How do you solve #2x^2+5x=0# using the quadratic formula?

Answer 1

Express in the form #ax^2+bx+c=0# then apply the formula to find:

#x = 0" "# or #" "x = -5/2#

Given:

#2x^2+5x=0#

We can write this equation as follows:

#2x^2+5x+0 = 0#

This takes the following form:

#ax^2+bx+c = 0#
with #a=2#, #b=5# and #c=0#

Its roots can be found using the quadratic formula:

#x = (-b+-sqrt(b^2-4ac))/(2a)#
#color(white)(x) = (-5+-sqrt((-5)^2-4(2)(0)))/(2*2)#
#color(white)(x) = (-5+-sqrt(25))/4#
#color(white)(x) = (-5+-5)/4#

Thus, one root is:

#x = (-5+5)/4 = 0#

and the other is:

#x = (-5-5)/4 = -10/4 = -5/2#
#color(white)()# Footnote

In this case, you really wouldn't want to use the quadratic formula.

Instead note that both terms are divisible by #x#, so it factors like this:
#0 = 2x^2+5x = x(2x+5)#
Which has solutions #x=0# and #x=-5/2#
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 the quadratic equation (2x^2 + 5x = 0) using the quadratic formula, which is (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}), where (a), (b), and (c) are the coefficients of the quadratic equation (ax^2 + bx + c = 0), follow these steps:

  1. Identify the values of (a), (b), and (c): (a = 2), (b = 5), and (c = 0).

  2. Substitute these values into the quadratic formula: (x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 2 \cdot 0}}}}{{2 \cdot 2}}).

  3. Simplify inside the square root: (x = \frac{{-5 \pm \sqrt{{25}}}}{{4}}).

  4. Take the square root of (25): (x = \frac{{-5 \pm 5}}{{4}}).

  5. Solve for both possible values of (x): (x_1 = \frac{{-5 + 5}}{{4}} = \frac{0}{4} = 0), (x_2 = \frac{{-5 - 5}}{{4}} = \frac{{-10}}{{4}} = -\frac{5}{2}).

Therefore, the solutions to the equation (2x^2 + 5x = 0) are (x = 0) and (x = -\frac{5}{2}).

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