Answer:
[tex]x_{1} =-5\\and \\x_{2} =-3[/tex]
Step-by-step explanation:
Solve by using factoring ------->
rewrite the expresion
x^2+8x+15=0
x^2+5x+3x+15=0
factor out x from the expression
x^2+5x+3x+15=0
xx(x+5)+3x+15=0
xx(x+5)+3(x+5)=0
factor out x+5 from expression
(x+5)x(x+3)=0
when the product of factors equals 0, at least one factor is 0
x+5=0
x+3=0
solve the equation for x
x = -5
x = -3
the equation has 2 solutions
[tex]x_{1} =-5, x_{2} =-3[/tex]
Quadratic formula
[tex]x=\frac{-8+\sqrt{8^{2} -4x1x15} }{2x1}[/tex]
any expression multiplied by 1 remains the same
[tex]x=\frac{-8+\sqrt{8^{2}-4x15 } }{2}[/tex]
evaluate the power
[tex]x=\frac{-8+\sqrt{64-4x15} }{2}[/tex]
multiply the numbers
[tex]x=\frac{-8+\sqrt{64-60} }{2}[/tex]
subtract the numbers
[tex]x=\frac{8+\sqrt{4} }{2}[/tex]
calculate the square root
[tex]x=\frac{-8+2}{2}[/tex]
write solution with a + sign and a - sign
[tex]x=\frac{-8+2}{2} \\x=\frac{-8-2}{2}[/tex]
calculate the value
[tex]x=-3\\x=-5[/tex]
the equation has 2 solutions
[tex]x=-3\\x=-5 \\and\\x_{1} =-5\\x_{2} =-3[/tex]
