Answer:
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One x- value of the solution is : -2 or -8
<h3>What is an equation?</h3>
An Equation is an algebraic statement that shows that two quantities are equal.
Analysis:
for one x-value of a solution, f(x) = g(x)
+ 7x -24 = -3x - 40
+7x +3x -24 +40 = 0
+ 10x +16 = 0
+8x +2x +16 = 0
x(x+8) +2(x+8) = 0
(x+2)(x+8) = 0
x = -2 or -8
In conclusion, the values of x are -2 or -8
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The factors illustrate they the sides of the rectangles are:
- (x - 1)(x - 2)
- (2x - 3)(x + 2)
<h3>How to get the factors?</h3>
The first equation given is x² - 3x + 2.
= x² - 3x + 2.
= x² - x - 2x + 2
= x(x - 1) - 2(x - 1)
= (x - 1)(x - 2)
Therefore, the side lengths are (x - 1) and (x - 2).
In the rectangular figure, the length and width should be the expressions above.
The second equation given is 2x² + x - 6.
= 2x² + x - 6.
= 2x² + 4x - 3x - 6
= 2x(x + 2) - 3(x + 2)
= (2x - 3)(x + 2)
Therefore, the side lengths are (2x - 3) and (x + 2).
In the rectangular figure, the length and width should be the expressions above.
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The answer is 16 if you solve it, because the square root of 64 is 8 and 2 * 8 = 16
