# Use two different methods to find the solution for x in the equation 2x^2 -7x + 6=0.

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### 2 Answers

The equation can be solved by determining the factors or by the use of the quadratic formula.

By determining factors:

2x^2 - 7x + 6 = 0

=> 2x^2 - 4x - 3x + 6 = 0

=> 2x(x - 2) - 3(x - 2) = 0

=> (2x - 3)(x - 2) = 0

2x - 3 = 0

=> x = 3/2

x - 2 = 0

=> x = 2

By using the quadratic formula:

The roots of ax^2 + bx + c = 0 are given by x1 = [-b + sqrt(b^2 - 4ac)]/2a and x2 = [-b - sqrt(b^2 - 4ac)]/2a

In 2x^2 - 7x + 6 = 0

a = 2 , b = -7 and c = 6

x1 = 7/4 + sqrt (49 - 48)/ 4

=> 7/4 + 1/4 = 8/4 = 2

x2 = 7/4 - 1/4 = 6/4 = 3/2

**The roots of 2x^2 - 7x + 6 = 0 are x = 2 and x = 3/2**

We have the quadratic equation: 2x^2 - 7x + 6 = 0

We can solve using the quadratic formula or by factoring.

1. using the quadratic formula:

x = [ -b +- sqrt(b^2-4ac)]/ 2a

==> x1= [ 7 + sqrt(49-4*2*6 ] / 4

= [ 7+ sqrt1 ) / 4 = 8/4 = 2

==> x2= ( 7-1)/4 = 6/4 = 3/2

2. Solve using factoring.

==> 2x^2 - 7x + 6 = ( 2x-3)(x-2)

==> x1= 3/2

==> x2= 2

**Then the solution is x = { 2, 3/2}**