Answer:
(a) 1
(b) 1
(c) 3.03
Step-by-step explanation:
The given quadratic equation is
Subtract 27 from both sides.
Taking out common factor.
Divide both sides by 4.
If an expression is , then we need to add , to make it perfect square.
Here, b=2, so
Add 1 on both sides.
Taking square root on both sides.
Subtract 1 from both sides.
and
and
Only one solution is positive.
Greatest solution is 3.031, therefore the approximate value of this solution is 3.03.
Answer:
Step-by-step explanation:
The given expression is
x^{2}+2x+7=21
To solve this expression, we need to pass all terms to the left side
[tex]x^{2}+2x+7=21\\x^{2}+2x+7-21=0\\x^{2}+2x-14=0[/tex]
Now, we solve the equation using the quadratic formula
[tex]x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac} }{2a}[/tex]
Where
[tex]a=1\\b=2\\c=-14[/tex]
Replacing these values, we have
[tex]x_{1,2}=\frac{-2\±\sqrt{2^{2}-4(1)(-14)} }{2(1)}\\x_{1,2}=\frac{-2\±\sqrt{4+56} }{2}=\frac{-2\±\sqrt{60} }{2} \\x_{1}\approx 2.9\\x_{2}\approx -4.9[/tex]
Therefore, this quadratic equation has only 1 positive solution, and the greatest solution is 2.87, rounded to the nearest hundredth.
