X^2+3x=24, halve the linear coefficient, square it, and add it to both sides

In this case (3/2)^2=2.25

x^2+3x+2.25=26.25 now the left side is a perfect square...

(x+1.5)^2=26.25 take the square root of both sides

x+1.5=±√26.25 subtract 1.5 from both sides

x=-1.5±√26.25

x=-1.5-√26.25 and -1.5+√26.25

x≈ -6.62 and 3.62

**Answer:**

<h3>5</h3>

**Step-by-step explanation:**

Find the complete question attached

The factor of 90 is as shown;

2 | 90

3 | 45

3 | 15

5 | 5

| 1

Hence the prime factorization of 90 is 2 * 3 * 3 * 5

90 = 2 * 3² * <u>**5**</u>

<em>**The number that completes the prime factorization is 5**</em>

X+y+z=180

Since y+z=5x, x+5x=180, so x=30

So,

30+y+z=180

y+z=150

Since z=y+24, y+y+24=150

2y=126

y=63

30+63+z=180

z=87

So x=30, y=63, z=87

**Answer:**

13 & 48

**Step-by-step explanation:**

Hope that helps!

**Answer:**

**($20/gal)r + ($30/gal)b ≤ $250**

**r + b ≤ 10 (gallons)**

**Step-by-step explanation:**

Represent the amount of red paint by r and that of blue point by b.

Olivia must cover 5000 ft^2 with paint, which comes out to 5000/500, or 10, gallons total of red and blue paint. The corresponding inequality is

r + b ≤ 10 (gallons)

She has onlyl $250 to spend. Therefore, the following must hold true:

($20/gal)r + ($30/gal)b ≤ $250

The required sysstem of inequalities is thus

**($20/gal)r + ($30/gal)b ≤ $250**

**r + b ≤ 10 (gallons)**