Answer:
12. [tex]x=-3\frac{1}{2}, x = 6[/tex]
15. [tex]4[/tex]
Step-by-step explanation:
12. [tex]2x^2-5x=42[/tex]
To solve this quadratic equation, we will put all the variables and constants on one side of the equation and factorize it.
[tex]2x^2-5x-42=0[/tex]
[tex]2x^2-12x+7x-42=0[/tex]
[tex]2x(x-6)+7(x-6)=0[/tex]
[tex](2x+7)(x-6)=0[/tex]
[tex]x=-\frac{7}{2}, x = 6[/tex]
[tex]x=-3\frac{1}{2}, x = 6[/tex]
Therefore, the solutions to the given expression are 3(1/2) and 6.
15. [tex]3x=8+\sqrt{3x+4}[/tex]
[tex]3x-8=\sqrt{3x+4}[/tex]
Squaring both the sides to get:
[tex](3x-8)^2=(3x+4)^2[/tex]
[tex]9x^2-48x+64=3x+4[/tex]
[tex]9x^2-51x+60=0[/tex]
[tex]3(3x^2-17x+20)=0[/tex]
[tex]3x^2-17x+20=0[/tex]
[tex]3x^2-12x-5x+20=0[/tex]
[tex]3x(x-4)-5(x-4)=0[/tex]
[tex]x=\frac{3}{5} (ignore), x=4[/tex]
Therefore, the solution to the given expression is 4.
