A rectangle's width is x and its length is 2x-1. Its area is 21. Find its dimensions.

my work so far:

21 = x(2x +1)
21 = 2x^2 + x

I was wondering how I would continue to solces this problem.

Check your sign error: 21 = x(2x-1)

To solve the equation 21 = 2x^2 + x, you need to rearrange it into a quadratic equation.

First, bring all the terms to one side of the equation:
2x^2 + x - 21 = 0

Now, you can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, factoring is the most suitable method.

The equation can be factored as follows:
(2x - 3)(x + 7) = 0

Now, set each factor equal to zero and solve for x:
2x - 3 = 0 or x + 7 = 0

Solving each equation, you get:
2x = 3 or x = -7

Since the length of a rectangle cannot be negative, we disregard the negative solution. Thus, x = 3/2.

Now, to find the width and length of the rectangle, substitute the value of x back into the expressions given for width and length:

Width (x) = 3/2
Length (2x - 1) = 2(3/2) - 1 = 3 - 1 = 2

Therefore, the dimensions of the rectangle are width = 3/2 and length = 2.

To continue solving the problem, you have successfully set up the equation: 21 = 2x^2 + x. Now, let's simplify the equation by rearranging it into the standard quadratic form, ax^2 + bx + c = 0.

Start by subtracting 21 from both sides of the equation:
2x^2 + x - 21 = 0

Now, the equation is in the standard quadratic form. To solve it, you can either factor it or use the quadratic formula. In this case, factoring may be the most efficient method.

To factor the quadratic equation, look for two numbers that multiply to give you -42 (the product of 2 and -21) and add up to 1 (the coefficient of the x term). After some trial and error, you can determine that the numbers are 7 and -6.

So, you can rewrite the equation in factored form:
(2x - 7)(x + 6) = 0

Now, set each factor equal to zero and solve for x:
2x - 7 = 0 or x + 6 = 0

Solving these two equations separately will give you two possible values for x:
2x - 7 = 0
2x = 7
x = 7/2
x = 3.5

and

x + 6 = 0
x = -6

Since the length of a rectangle cannot be negative, we can disregard the solution x = -6.

Therefore, the width of the rectangle (x) is 3.5, and the length (2x - 1) can be calculated as follows:
length = 2x - 1
length = 2(3.5) - 1
length = 7 - 1
length = 6

Hence, the dimensions of the rectangle are a width of 3.5 units and a length of 6 units.

The same way I already showed you ...