Answer:
[tex]\dfrac{-5 + \sqrt{37}}{2}[/tex]
Step-by-step explanation:
To find the value of x :
1. The area of the square is [tex]x \times x = x^2 .[/tex]
2. The area of the rectangle is [tex](2x - 1) \times (x + 3).[/tex]
Since both areas are the same:
[tex]x^2 = (2x - 1)(x + 3)[/tex]
3. Expand and simplify:
[tex]x^2 = 2x^2 + 6x - x - 3\\\\x^2 = 2x^2 + 5x - 3\\\\0 = x^2 + 5x - 3[/tex]
4. Use the quadratic formula [tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex], where a = 1 , b = 5 , and c = -3 :
[tex]x = \dfrac{-5 \pm \sqrt{25 + 12}}{2}\\\\x = \dfrac{-5 \pm \sqrt{37}}{2}[/tex]
Since x must be positive:
x [tex]= \dfrac{-5 + \sqrt{37}}{2}[/tex]
So,[tex]x \approx 1.54[/tex] (for easier understanding, but the exact answer is [tex](\dfrac{-5 + \sqrt{37}}{2}).[/tex]
