-2x(x+3)-(x+1)(x-2)=
-2x(x+3)-(x+1)(x-2)=
-2x2 -6x -x2+x+2=
-3x2-5x+2= check that
Nothing hard about this ...
-2x(x+3) - (x+1)(x-2)
-2x^2-6x - (x^2-x-2)
-2x^2-6x-x^2+x+2
-3x^2-5x+2
To solve the equation -2x(x+3)-(x+1)(x-2) = 0, we need to simplify and then find the value(s) of x that satisfy the equation.
Step 1: Distribute using the distributive property:
-2x(x + 3) - (x + 1)(x - 2) = 0
Distributing the -2x, we get:
-2x * x - 2x * 3 - (x + 1)(x - 2) = 0
-2x^2 - 6x - (x + 1)(x - 2) = 0
Distribute the (x + 1) and (x - 2):
-2x^2 - 6x - (x * x + x * -2 + 1 * x + 1 * -2) = 0
-2x^2 - 6x - (x^2 - 2x + x - 2) = 0
-2x^2 - 6x - (x^2 - x - 2) = 0
Simplifying further:
-2x^2 - 6x - x^2 + x + 2 = 0
-2x^2 - x^2 - 6x + x + 2 = 0
-3x^2 - 5x + 2 = 0
Step 2: Rearrange the equation to set it equal to zero:
-3x^2 - 5x + 2 = 0
Step 3: You can now solve this equation using factoring, completing the square, or the quadratic formula. For this particular equation, since it doesn't factor easily, we will solve it using the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation -3x^2 - 5x + 2 = 0, we have a = -3, b = -5, and c = 2.
Substituting these values into the quadratic formula, we get:
x = (-(-5) ± √((-5)^2 - 4(-3)(2))) / (2(-3))
x = (5 ± √(25 + 24)) / (-6)
x = (5 ± √(49)) / (-6)
x = (5 ± 7) / (-6)
Simplifying further, we have two possible solutions:
x = (5 + 7) / (-6) = 12 / (-6) = -2
x = (5 - 7) / (-6) = -2 / (-6) = 1/3
Therefore, the equation is satisfied when x is equal to -2 or 1/3.