Answer:

1. x² +6x-3= O

Move the constant term to the other side of the equation:

x²+6x=3

To complete the square, take half of the coefficient of the linear term (6x), square it, and add it to both sides of the equation. Half of 6x is 3, and 32 is 9: x²+6x+9=3+9

x²+6x+9=12

(x+3)=12

x+3= ±√12

x = -3± √12

x= -3 ± 2√3

x=-3+2/3 and x = - 3 - 2√3

2. x+4x-3= O

Move the constant term to the other side of the equation:

x²+4x=3

To complete the square, take half of the coefficient of the linear term (4x), square it. and add it to both sides of the equation. Half of 4x is 2x, and 2x² is 4:

x²+4x+4=3+4

x²+4x+4=7

(x+2)=7

x+2=±√7

x= -2±√7

x=-2+ √7 and x = -2-√7.

3. 2x² - 16x + 1 = 0

Divide the entire equation by the coefficient of x², which is 2, to make the coefficient of x² equal to 1: x²-8x+1/2=0

x²-8x=-1/2

To complete the square, take half of the coefficient of the linear term (-8x), square it. and add it to both sides of the equation. Half of -8x is-4x, and (-4x) is 16x²:

x²-8x+16=-1/2+16

x²-8x+16=31/2

(x-4)=31/2

x-4=± √(31/2)

Add 4 to both sides:

x=4±√(31/2)

x=4+/62/2 and x = 4-√62/2.

Step-by-step explanation:

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