HELP ME PLEASE! (X+2)(2X-5)=-9?

2x^2 - 5x + 4x - 10 = 9
2x^2 - x - 19 = 0

use the quadr eqaution to solve for x.


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2x² - x - 10 = - 9
2x² - x - 1 = 0
(2x + 1)(x - 1) = 0
x = - 1/2 , x = 1

(x + 2)(2x - 5) = -9
x*2x + 2*2x - x*5 - 2*5 + 9 = 0
2x^2 + 4x - 5x - 10 + 9 = 0
2x^2 - x - 1 = 0
2x^2 + x - 2x - 1 = 0
(2x^2 + x) - (2x + 1) = 0
x(2x + 1) - 1(2x + 1) = 0
(2x + 1)(x - 1) = 0

2x + 1 = 0
2x = -1
x = -1/2 (-0.5)

x - 1 = 0
x = 1

∴ x = -1/2 (-0.5) , 1

(x+2)(2x-5)=-9
2x^2-x-10=-9
2x^2-x-1=0
(2x+1)(x-1)=0
x=-1/2 and 1

This is a case of completing the square.

Expand out (x + 2)(2x - 5) = -9 to get 2x^2 + 4x - 5x -10 = -9, which is simplified to 2x^2 - x - 10 = -9.

Add 10 to both sides: 2x^2 - x = 1
Divide both sides by 2: x^2 - 1/2 x = 1/2
Complete the square: if you add 1/16 to both sides, it will look like this:
x^2 - 1/2 x + 1/16 = 9/16
Since x^2 - 1/2 x + 1/16 = (x - 1/4)^2,
(x- 1/4) ^2 = 9/16
Take the square root of both sides: x - 1/4 = 3/4

Can you solve from there for x, using a simple addition to both sides?

First multiply out the left side:

(X + 2) * (2X - 5) = -9

First, outside, inside, last

2x^2 - 5x + 4x - 10 = -9

Combine the x terms

2x^2 -x - 10 = -9

Add 9 to both sides to get the equation into quadratic form:

2x^2 - x - 1 = 0

Solve with the quadratic equation:

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

using a = 2, b = -1, and c = -1

x = [1 +- sqrt(-1^2 - 4 * 2 * -1)] / 2 * 2

[corrected]
x = [1 +- sqrt(1 - -8)] / 4

x = [1 +- sqrt(9)] / 4

x = [1 +- 3] / 4

x = 4 / 4 = 1
and
x = -2 / 4 = -1/2

The roots are -1/2 and 1.

Assuming you're solving for x,
I would multiply it out first so I could try to get it into quadratic formula form and make it equal 0.
(X+2)(2X-5)= -9
2x^2 - 5x + 4x - 10 = -9
2x^2 -x -1 = 0

then solve it out again.
(2x + 1)(x - 1) = 0

2x +1 = 0 ----> x = -1/2
x -1 = 0 ------> x = 1

so x = 1 or -1/2

2x^2-5x+4x-10=-9

2x^2 -x-10+9=0

2x^2 -x-1 = 0

2x^2 -2x + 1x -1 = 0

2x (x-1) + 1(x-1) = 0

(2x+1) (x-1) = 0

X = 1 and X = -1/2

2x^2-5x+4x-10=-9

2x^2 -x-10+9=0

2x^2 -x-1 = 0

2x^2 -2x + 1x -1 = 0

2x (x-1) + 1(x-1) = 0

(2x+1) (x-1) = 0

X = 1 and X = -1/2

2x^2-5x+4x-10=-9

2x^2 -x-10+9=0

2x^2 -x-1 = 0

2x^2 -2x + 1x -1 = 0

2x (x-1) + 1(x-1) = 0

(2x+1) (x-1) = 0

X = 1 and X = -1/2