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Anvisha [2.4K]
3 years ago
10

Use the quadratic formula to solve the equation.

Mathematics
2 answers:
Sergeeva-Olga [200]3 years ago
7 0

ANSWER

x =  \frac{ 5  - \sqrt{ 5} }{4}  \: or  \:  \: x =  \frac{ 5 +  \sqrt{ 5} }{4}

EXPLANATION

The given quadratic equation is

4 {x}^{2}  - 10x + 5 = 0

We compare this to

a {x}^{2}  + bx + c = 0

to get a=4, b=-10, and c=5.

The quadratic formula is given by

x =  \frac{ - b \pm \sqrt{ {b}^{2}   - 4ac} }{2a}

We substitute these values into the formula to get:

x =  \frac{ -  - 10 \pm \sqrt{ {( - 10)}^{2}   - 4(4)(5)} }{2(4)}

This implies that

x =  \frac{ 10 \pm \sqrt{ 100  - 80} }{8}

x =  \frac{ 10 \pm \sqrt{ 20} }{8}

x =  \frac{ 10 \pm2 \sqrt{ 5} }{8}

x =  \frac{ 5 \pm \sqrt{ 5} }{4}

The solutions are:

x =  \frac{ 5  - \sqrt{ 5} }{4}  \: or  \:  \: x =  \frac{ 5 +  \sqrt{ 5} }{4}

meriva3 years ago
4 0

Answer:

\large\boxed{x=\dfrac{5-\sqrt5}{4},\ x=\dfrac{5+\sqrt5}{4}}

Step-by-step explanation:

\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac

\text{We have the equation:}\ 4x^2-10x+5=0\\\\a=4,\ b=-10,\ c=5\\\\b^2-4ac=(-10)^2-4(4)(5)=100-80=20>0\\\\x=\dfrac{-(-10)\pm\sqrt{20}}{2(4)}=\dfrac{10\pm\sqrt{4\cdot5}}{8}=\dfrac{10\pm\sqrt4\cdot\sqrt5}{8}=\dfrac{10\pm2\sqrt5}{8}\\\\=\dfrac{2(5\pm\sqrt5)}{8}=\dfrac{5\pm\sqrt5}{4}

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A grocery store has 120 bottles of spring
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Question:

A grocery store has 120 bottles of spring water in stock.  The store orders bottles of spring water in cases of 24.  The store wants to order enough cases of spring water so it has more than 500 bottles in stock.  Which inequality best models this situation?

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Step-by-step explanation:

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The store wants  to order enough cases of spring water so  that it has over 500 bottles in stock.

So there are already 120 bottles in stock .

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C. 39.6

<em>good luck, i hope this helps :)</em>

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