Quadratic Equations need help?

Question

1. 6x(x-1)=21-x ,solve by factoring

2. x2=3/4x-1/8 ,solve by completing the square

x2 is x squared

need solutions with answers

Answer 1

PROBLEM 1:
6x(x-1) = 21-x

Multiply the 6x through the parentheses:
6x² - 6x = 21 - x

Add x to both sides:
6x² - 5x = 21

Subtract 21 from both sides:
6x² - 5x - 21 = 0

Now factor:
(2x + 3)(3x - 7) = 0

So either 2x + 3 = 0 or 3x - 7 = 0

This leads to x = -3/2 or x = 7/3

PROBLEM 2:

x² = 3/4x - 1/8

Get everything on one side:
x² - 3/4x + 1/8 = 0

Take the x-term (-3/4), divide it in half (-3/8) and square it (9/64). Add and subtract this amount.

(x² - 3/4x + 9/64) - (9/64 + 1/8) = 0

The first part in parentheses is a perfect square now, so rewrite:

(x - 3/8)² - (9/64 + 1/8) = 0

Simplify the second part:
(x - 3/8)² - (9/64 + 8/64) = 0
(x - 3/8)² - 17/64 = 0

Now move this to the other side:
(x - 3/8)² = 17/64

The the square root of both sides:
x - 3/8 = +/- sqrt(17/64)

x = 3/8 +/- sqrt(17/64)

Answer 2

1- 6x^2 - 6x + x - 21 = 0
6x^2 - 5x - 21 = 0
6x^2 - 14x + 9x -21 = 0
2x( 3x - 7) + 3(3x - 7) =0
(3x-7)(2x +3) = 0
x= 7/3 , - 3/2

2- x^2 - (3/4)x + 1/8 =0
( x - 3/8 )^2 - 9/64 + 1/8 = 0
(x - 3/8 )^2 = 5/64
( x - 3/8) = +/- (5)^(1/2)/8
x={ 3 +/- (5)^(1/2) }/8