5)Solve 2x2 +6x = 4 by completing the square.

6)Solve 3x2 - 6x- 24 = 0 using the quadratic formula.

7)The area of a circle is 25 in^2. What is the radius, including the units? Area of a circle is ¢³r^2.

8)The 3 sided triangle has an area of 14 in^2. Determine the lengths of the sides of the triangles. Remember that the area of a triangle is ¨ö bh. Bottom length is x+3 the side length is x

5. 2x2 + 6x = 4

Divide Fq by 2:
x2 + 3x = 2
x2 + 3x + (3/2)^2 = 2 + 9/4
x2 + 3x + 9/4 = 8/4 + 9/4 = 17/4
x2 + 3x + 9/4 - 17/4 = 0
x2 + 3x -8/4 = 0
x2 + 3x - 2 = 0
Use Quadratic Formula:
X = 0.562, and -3.562.

6. 3x2 - 6x - 24 = 0
Divide Eq by 3:
x2 - 2x - -8 = 0
Solve using Quadratic formula:

7. A = pi*r^2 = 25in^2
3.14r^2 = 25
r^2 = 25/3.14 = 7.96
r = 2.82 Inches.

8. A = (bh)/2 = 14 In^2
((x+3)x)/2 = 14
Multiply Eq by 2:
(x+3)x = 28
x^2 + 3x = 28.
x^2 + 3x - 28 = 0
(x+7)(x-4) = 0
x+7 = 0
x = -7.

x-4 = 0
x=4.

Solution set: X = -7, and 4.

5) To solve the equation 2x^2 + 6x = 4 by completing the square, follow these steps:

Step 1: Move the constant term to the right side of the equation:
2x^2 + 6x - 4 = 0

Step 2: Divide the entire equation by the coefficient of x^2 (in this case, 2) to make the leading coefficient 1:
x^2 + 3x - 2 = 0

Step 3: Take half of the coefficient of x (in this case, 3) and square it:
(3/2)^2 = 9/4

Step 4: Add the result from Step 3 to both sides of the equation:
x^2 + 3x + 9/4 - 2 = 9/4
x^2 + 3x + 1/4 = 9/4

Step 5: Rewrite the left side of the equation as a perfect square:
(x + 3/2)^2 = 9/4

Step 6: Take the square root of both sides, considering both positive and negative square roots:
x + 3/2 = ±√(9/4)
x + 3/2 = ±3/2

Step 7: Solve for x by isolating it on each side of the equation:
x = -3/2 ± 3/2

Therefore, the solutions to the equation 2x^2 + 6x = 4 are x = -3 and x = 1.

6) To solve the equation 3x^2 - 6x - 24 = 0 using the quadratic formula, follow these steps:

Step 1: Identify the coefficients a, b, and c in the equation:
a = 3
b = -6
c = -24

Step 2: Substitute the coefficients into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
x = (-(-6) ± √((-6)^2 - 4(3)(-24))) / (2(3))

Step 3: Simplify the equation inside the square root:
x = (6 ± √(36 + 288)) / 6
x = (6 ± √324) / 6
x = (6 ± 18) / 6

Step 4: Solve for x by isolating it on each side of the equation:
x = (6 + 18) / 6 or x = (6 - 18) / 6
x = 24 / 6 or x = -12 / 6
x = 4 or x = -2

Therefore, the solutions to the equation 3x^2 - 6x - 24 = 0 are x = 4 and x = -2.

7) To find the radius of a circle when given the area, follow these steps:

Step 1: Recall the formula for the area of a circle: A = πr^2

Step 2: Substitute the given area into the formula: 25 = πr^2

Step 3: Divide both sides of the equation by π to isolate r^2:
r^2 = 25 / π

Step 4: Take the square root of both sides to solve for r:
r = √(25 / π)

Step 5: Simplify the expression and include the units:
r ≈ √(25 / 3.14) ≈ 2.82 inches

Therefore, the radius of the circle with an area of 25 in^2 is approximately 2.82 inches.

8) To determine the lengths of the sides of a triangle when given its area and the lengths of the base and one side, follow these steps:

Step 1: Recall the formula for the area of a triangle: A = 1/2 * base * height

Step 2: Substitute the given area into the formula: 14 = 1/2 * (x + 3) * x

Step 3: Simplify the equation:
14 = 1/2 * (x^2 + 3x)
28 = x^2 + 3x

Step 4: Rearrange the equation to form a quadratic equation equal to zero:
x^2 + 3x - 28 = 0

Step 5: Solve the quadratic equation using factoring, completing the square, or the quadratic formula:
(x - 4)(x + 7) = 0

Step 6: Set each factor equal to zero and solve for x:
x - 4 = 0 or x + 7 = 0
x = 4 or x = -7

Therefore, the possible lengths of the sides of the triangle are x = 4 inches and x = -7 inches.