Solve the equation by completing the square. Round to the nearest hundredth if necessary.

x2 + 3x – 5 = 0


A.1.19, –4.19


B.–8.75, 5.75


C.1.66, 2.69


D.1.05, –4.05

1.C

2.C
3.B
4.D
5.B

"answers" is 100% correct, I just completed the quick check, but if anyone needs specific answers here you go, and thank you

1. 4, -2
2. 30.25
3. -12, 8
4. There is no solution
5. 8 in.

this is for Connexus, Unit 5 Lesson 5 8th grade honors

;-(

x^2+3x-5 = 0

x^2+3x+(3/2)^2 = 5+(3/2)^2
(x+3/2)^2 = 29/4
x+3/2 = ±√29/2
x = (-3±√29)/2

Hmm, completing the square, huh? Well, let's see if we can make this equation more fun!

First, let's take a look at the equation x^2 + 3x - 5 = 0. To complete the square, we want to make the left side a perfect square trinomial.

Step 1: Add the square of half the coefficient of the x term to both sides.
So, half of 3 is 1.5, and the square of 1.5 is 2.25. So, let's add 2.25 to both sides of the equation.

x^2 + 3x + 2.25 - 5 = 2.25
x^2 + 3x + 2.25 - 5 = 2.25

Step 2: Now, let's rewrite the left side as a perfect square trinomial.
We can rewrite the left side as (x + 1.5)^2 - 5 = 2.25.

Step 3: Let's simplify the equation.
(x + 1.5)^2 - 5 = 2.25
(x + 1.5)^2 = 7.25

Step 4: Take the square root of both sides.
x + 1.5 = ±√7.25

Now, if we solve for x, we get:

x = -1.5 ± √7.25

And if we round to the nearest hundredth, we get:

x = -1.19 and -4.82

So, the answer is NOT any of the options given. Looks like we have an equation that's too cool for those options!

To solve the equation by completing the square, follow these steps:

Step 1: Move the constant term to the right side of the equation:
x^2 + 3x = 5

Step 2: Take half the coefficient of the x-term, square it, and add it to both sides of the equation:
x^2 + 3x + (3/2)^2 = 5 + (3/2)^2
x^2 + 3x + 9/4 = 5 + 9/4

Step 3: Simplify and convert the right side to a common denominator:
x^2 + 3x + 9/4 = 20/4 + 9/4
x^2 + 3x + 9/4 = 29/4

Step 4: Rewrite the left side as a perfect square trinomial:
(x + 3/2)^2 = 29/4

Step 5: Take the square root of both sides, remembering to include both the positive and negative square root on the right side:
x + 3/2 = ±√(29/4)

Step 6: Solve for x by subtracting 3/2 from both sides:
x = -3/2 ± √(29/4)

Step 7: Simplify the square root and convert the fractions to decimals:
x ≈ -3/2 ± √(29/4)
x ≈ -1.5 ± √(7.25)
x ≈ -1.5 ± 2.69

Rounding to the nearest hundredth, we have:

x ≈ 1.19 or x ≈ -4.19

Therefore, the answer is A. 1.19, -4.19.