Answer:
[tex]y=-\frac{1}{2}[/tex]
Step-by-step explanation:
Given: [tex]2y+5=\sqrt{15-2y}\\[/tex]
To get rid of a square root, square both sides of the equation.
[tex]2y+5=\sqrt{15-2y}\\(2y+5)^2=(\sqrt{15-2y})^2\\(2y+5)^2=15-2y[/tex]
Factor [tex](2y+5)^2[/tex] by FOILing.
[tex](2y+5)(2y+5)=15-2y\\4y^2+20y+25=15-2y[/tex]
Add 2y to both sides and subtract 15 by both sides to get one side equal to 0.[tex]4y^2+20y+25=15-2y\\4y^2+22y+10=0[/tex]
Use the quadratic formula, or use a graphing calculator.
[tex]y=-\frac{1}{2}[/tex]
