Answer:
16
Step-by-step explanation:
To solve a quadratic equation by using the completing the square method, the coefficient of the square term i.e x² must be one (1).
Therefore, we would have to first make the coefficient of x² to be equal to 1.
4x² + 24x + 8 = 32
We would simplify the equation;
4x² + 24x = 32 - 8
4x² + 24x = 24
Divide all through by 4;
x² + 8x = 24
The value to be added = (8/2)² = 4² = 16
x² + 8x + 16 = 8 + 16
x² + 4x + 4x + 16 = 24
x(x + 4) + 4(x + 4) = 24
(x + 4)² = 24
Taking the square root of both sides;
x + 4 = ± 4.9
x = -4 ± 4.9
x = -4 + 4.9 = 0.9
or
x = -4 - 4.9 = - 8.9
<em>Therefore, 16 must be added to solve the quadratic equation by completing the square method. </em>
If we let x and y represent length and width, respectively, then we can write equations according to the problem statement.
.. x = y +2
.. xy = 3(2(x +y)) -1
This can be solved a variety of ways. I find a graphing calculator provides an easy solution: (x, y) = (13, 11).
The length of the rectangle is 13 inches.
The width of the rectangle is 11 inches.
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Just so you're aware, the problem statement is nonsensical. You cannot compare perimeter (inches) to area (square inches). You can compare their numerical values, but the units are different, so there is no direct comparison.
Answer:

Step-by-step explanation:
