SOLUTION: I have been trying to figure out this math problem and I can't get the answer. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Pr

Question 167137This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been trying to figure out this math problem and I can't get the answer. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Problem Solving Using Polynomial Equations
Solve each problem. If there are two correct answers, give both of them.
A rectangle is 15cm wide and 18cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116cm^2 less than the area of the original. Find the dimensions of the new rectangle. This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A rectangle is 15cm wide and 18cm long. If both dimensions are decreased by the same amount, the area of the new rectangle formed is 116cm^2 less than the area of the original. Find the dimensions of the new rectangle.
.
Let x = amount decreased
.
new width = 15-x
new length = 18-x
.
(15-x)(18-x) = 116
270-15x-18x+x^2 = 116
270-33x+x^2 = 116
154-33x+x^2 = 0
x^2-33x+154 = 0
.
Using the quadratic equation to solve we get:
x = {27.374, 5.626}
.
We can toss out the 27.374 leaving us with
x = 5.626
.
new width = 15-x = 15-5.626 = 9.374 inches
new length = 18-x = 18-5.626 = 12.374 inches
.
Solution: new rectangle is 9.374 by 12.374 inches
.
Details of quadratic:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=473 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 27.3742815854658, 5.62571841453423. Here's your graph:

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