Express in A+Bi form?

Question

1.x2-4x=-13
2.2x^2=-3(2x+3)
3.3x^2+3=5x
Help?!?

Answer 1

1). x² - 4x = -13

Add 13 to each side.

x² - 4x +13 = 0

Now solve the equation using the factor method.

Compare equation with standard from ax² + bx + c = 0 and write the coefficients.

a = 1, b = -4 and c = 13.

Quadratic formula: x=[-b±√(b²- 4ac)]/2a

Substitute a = 1, b = -4 and c = 13. in the Quadratic formula.

x = [-(-4)±√((-4)²- 4(1)(13))]/2(1)

x = [4 ±√(16 - 52)]/2

x = [4 ±√(-36)]/2

x = [4 ±√(i²36)]/2

x =[ 4 ±√(i²36)]/2

x = [4 ±i6]/2

Take out common term 2.

x = 2[2 ±i3]/2

x = [2 ±i3]

Therefore x = 2 + 3i or x = 2 - 3i.

A + Bi form is x = 2 + 3i or x = 2 - 3i.

 

Answer 2

2). 2x² = -3(2x + 3)

Distribute terms using distributive property:  a(b + c) = ab + ac

2x² = -6x - 9

Add 6x and 9 to each side

2x²+ 6x + 9 = 0

Now solve the equation using the factor method.

Compare equation with standard from ax² + bx + c = 0 and write the coefficients.

a = 2, b = 6 and c = 9.

Quadratic formula: x=[-b±√(b²- 4ac)]/2a

Substitute a = 2, b = 6 and c = 9 in the Quadratic formula.

x = [-(6)±√((6)²- 4(2)(9))]/2(2)

x = [-6 ±√(36 - 72)]/4

x = [-6 ±√(-36)]/4

x = [-6 ±√(i²36)]/4

x =[ -6 ±√(i²36)]/4

x = [-6 ±i6]/4

Take out common term 6.

x = 6[-1 ± i]/4

x = 3[-1 ±i]/2

Therefore x = 3[-1 + i]/2 or x = 3[-1 - i]/2

A + Bi form is x = -3/2 + 3i/2 or x = -3/2 - 3i/2

Answer 3

3). 3x² + 3 = 5x

Subtract 5x from each side.

3x²- 5x + 3 = 0

Now solve the equation using the factor method.

Compare equation with standard from ax² + bx + c = 0 and write the coefficients.

a = 3, b = -5 and c = 3.

Quadratic formula: x=[-b±√(b²- 4ac)]/2a

Substitute a = 3, b = -5 and c = 3 in the Quadratic formula.

x = [-(-5)±√((-5)²- 4(3)(3))]/2(3)

x = [5 ±√(25 - 36)]/6

x = [5 ±√(-11)]/6

x = [5 ±√(i²11)]/6

x = [5 ±i√11]/6

Therefore x = [5 + i√11]/6 or x = [5 - i√11]/6

A + Bi form is x = 5/6 + i√11/6 or x = 5/6 - i√11]/6.