Problem 1 :

x2 + 8x + 5 = 0

Problem 2 :

2x2 + 6x + 1 = 0

Problem 3 :

x2 + 2x = 2

Problem 4 :

x2 + 2 = 6x

Problem 5 :

3x2 + 2x – 2 = 0

Problem 6 :

x + ¹⁄ₓ = 3

Problem 7 :

(x + 2)(x – 1) = 5

Problem 8 :

x + ¹⁄₍ₓ ₊ ₂₎ = 4

Problem 9 :

(x + 1)2 = 3 – x2

Problem 10 :

Comparing ax2 + bx + c = 0 and x2 + 8x + 5 = 0 = 0, we get

a = 1, b = 8, c = 5

Substitute a = 1, b = 8 and c = 5.

x = -4 ± √11

x = -4 + √11  or  -4 - √11

2x2 + 6x + 1 = 0

From the above quadratic equation, we have

a = 2, b = 6, c = 1

Substitute the above values into the quadratic formula.

x2 + 2x = 2

Subtract 2 from both sides.

x2 + 2x - 2 = 0

From the above quadratic equation, we have

a = 1, b = 2, c = -2

Substitute the above values into the quadratic formula.

x = -1 ± √3

x = -1 + √3  or  -1 - √3

x2 + 2 = 6x

Subtract 6x from both sides.

x2 - 6x + 2 = 0

From the above quadratic equation, we have

a = 1, b = -6, c = 2

Substitute the above values into the quadratic formula.

x = 3 ± √7

x = 3 + √7  or  3 - √7

3x2 + 2x – 2 = 0

From the above quadratic equation, we have

a = 3, b = 2, c = -2

Substitute the above values into the quadratic formula.

x + ¹⁄ₓ = 3

Multiply both sides by x.

x(x + ¹⁄ₓ) = x(3)

x2 + 1 = 3x

Subtract 3x from both sides.

x2 - 3x + 1 = 0

From the above quadratic equation, we have

a = 1, b = -3, c = 1

Substitute the above values into the quadratic formula.

(x + 2)(x – 1) = 5

x2 - x + 2x - 2 = 5

x2 + x - 2 = 5

Subtract 5 from both sides.

x2 + x - 7 = 0

From the above quadratic equation, we have

a = 1, b = 1, c = -7

Substitute the above values into the quadratic formula.

x + ¹⁄₍ₓ ₊ ₂₎ = 4

Multiply both sides by (x + 2).

(x + 2)[x + ¹⁄₍ₓ ₊ ₂₎] = 4(x + 2)

x(x + 2) + (x + 2)[¹⁄₍ₓ ₊ ₂₎] = 4x + 8

x2 + 2x + 1 = 4x + 8

Subtract 4x and 8 from both sides.

x2 - 2x - 7 = 0

From the above quadratic equation, we have

a = 1, b = -2, c = -7

Substitute the above values into the quadratic formula.

x = 1 ± 2√2

x = 1 + 2√2  or  1 - 2√2

(x + 1)2 = 3 – x2

x2 + 2x + 1 = 3 – x2

2x2 + 2x + 1 = 3

Subtract 3 from both sides.

2x2 + 2x - 2 = 0

Divide both sides by 2.

x2 + x - 1 = 0

From the above quadratic equation, we have

a = 1, b = 1, c = -1

Substitute the above values into the quadratic formula.

(x + 2)(x + 1) = 3x(x - 1)

x2 + x + 2x + 2 = 3x2 - 3x

x2 + 3x + 2 = 3x2 - 3x

2x2 - 6x - 2 = 0

Divide both sides by 2.

x2 - 3x - 1 = 0

From the above quadratic equation, we have

a = 1, b = -3, c = -1

Substitute the above values into the quadratic formula.

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