Solve by factoring; 2x^2-9x-56=0?

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( 2x + 7 ) ( x - 8 ) = 0

x = - 7/2 , x = 8

2x^2-9x-56=0

2x^2-16x+7x-56=0

2x(x-8)+7(x-8)=0

(2x-7)(x-8)=0

x=3.5 or x=8

Good question

2x² - 9x - 56 = 0

2x² - (9+d)x + dx - 56 = 0

{ where 2:(9+d) = d:56 so d² + 9d - 112 = 0, (d+16)(d-7) = 0 so substitute either -16 or 7 for d }

2x² - (9+7)x + 7x - 56 = 0

2x² - 16x + 7x - 56 = 0

2x(x - 8) + 7(x - 8) = 0

(2x + 7)(x - 8) = 0

Solutions: x = -7/2 and x = 8

2x^2 - 9x - 56 = 0

(2x + 7)(x - 8) = 0

Solutions:

x = -7/2

x = 8

2x^2-9x-56=0

(2x+7)(x−8)=0

2x = -7

x = - 3.5

or

x = 8

2x^2 - 9x - 56 = 0

(2x + 7)(x - 8) = 0

Solutions:

x = -7/2

x = 8

Break up the middle term into two terms whose coefficients have a sum of -9 and a product of -56*2 = -112:

2x^2 - 16x + 7x - 56 = 0

Factor by grouping

2x(x - 8) + 7(x - 8) = 0

(2x + 7)(x - 8) = 0

Zero product rule:

2x + 7 = 0 or x - 8 = 0

2x = -7 or x = 8

x = -7/2 = -3.5 or x = 8

If you have trouble with the above, Complete the Square:

2x^2 - 9x = 56

x^2 - 4.5x = 28

x^2 - 4.5x + 5.0625 = 28 + 5.0625

(x - 2.25)^2 = 33.0625

x - 2.25 = +/- sqrt(33.0625)

x = 2.25 +/- 5.75

x = 8 or -3.5

Or use the Quadratic Formula:

x = (-(-9) +/- sqrt((-9)^2 - 4(2)(-56))) / (2*2)

x = (9 +/- sqrt(81 + 448)) / 4

x = (9 +/- sqrt(529)) / 4

x = (9 +/- 23) / 4

x = (32 or -14) / 4

x = 8 or -3.5

2x^2-9x-56=0

(2x + 7)(x - 8) = 0

2x + 7 = 0 , x - 8 = 0

x = - 7/2 and x = 8

x = - 7/2 and 8 answer//

If 2x^2 -9x -56 = 0 then (2x+7)(x-8) = 0 when factored and so x = -7/2 or x = 8

Learn how to use the quadratic equation formula.