# How do you solve #p^2 + 3p - 9 = 0# by completing the square?

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

Step 1: Incorporate and eliminate the perfect square element.

Next, square the outcome.

The original expression should then have this term added and subtracted.

P^2 + 3p + 9/4 -9/4-9 = 0#

- Compute the perfect square.

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

To solve the equation ( p^2 + 3p - 9 = 0 ) by completing the square, first move the constant term to the other side of the equation: ( p^2 + 3p = 9 ). Then, add the square of half the coefficient of ( p ) to both sides: ( p^2 + 3p + \left(\frac{3}{2}\right)^2 = 9 + \left(\frac{3}{2}\right)^2 ). This simplifies to ( p^2 + 3p + \frac{9}{4} = \frac{45}{4} ). Factor the left side as a perfect square trinomial: ( \left(p + \frac{3}{2}\right)^2 = \frac{45}{4} ). Take the square root of both sides: ( p + \frac{3}{2} = \pm \sqrt{\frac{45}{4}} ). Simplify: ( p + \frac{3}{2} = \pm \frac{3\sqrt{5}}{2} ). Finally, solve for ( p ): ( p = -\frac{3}{2} \pm \frac{3\sqrt{5}}{2} ).

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

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7