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jeka94
2 years ago
8

Using the quadratic formula to solve x2 = 5 – X, what are the values of X?

Mathematics
1 answer:
anygoal [31]2 years ago
4 0

Answer:

A)\:x=\frac{-1\pm\sqrt{21}}{2}

Step-by-step explanation:

x^2=5-x

<u>Add x from both sides:</u>

\longmapsto x^2+x=5-x+x

\longmapsto x^2+x=5

<u>Subtract 5 from both sides:</u>

\longmapsto x^2+x-5=5-5

\longmapsto x^2+x-5=0

Now, we'll use the quadratic formula to solve this problem: x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

\longmapsto x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\times \:1\cdot \left(-5\right)}}{2\times \:1}

\longmapsto \sqrt{1^2-4\times \:1\times \left(-5\right)}

\longmapsto 1^2=1

\longmapsto \sqrt{1+4\times \:1\times \:5}

<u>Multiply 4*1*5= 20</u>

\longmapsto \sqrt{1+20}

<u>Add 1 and 20= 21</u>

\longmapsto \sqrt{21}

\longmapsto x_{1,\:2}=\frac{-1\pm \sqrt{21}}{2\times \:1}

\longmapsto x_1=\frac{-1+\sqrt{21}}{2\times \:1}

\longmapsto \frac{-1+\sqrt{21}}{2\times \:1}

<u>Multiply 2 and 1= 2</u>

\longmapsto \frac{-1+\sqrt{21}}{2}

\longmapsto x_2=\frac{-1-\sqrt{21}}{2\times \:1}

\longmapsto \frac{-1-\sqrt{21}}{2\times \:1}

<u>Multiply 2 and 1= 2</u>

\longmapsto \frac{-1-\sqrt{21}}{2}

\longmapsto x=\frac{-1+\sqrt{21}}{2},\:x=\frac{-1-\sqrt{21}}{2}

\hookrightarrow x=\frac{-1\pm\sqrt{21}}{2}

________________________

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Answer:

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Step-by-step explanation:

3.75 - 3x ≤ 6

Subtract 3.75 on both sides.

- 3x ≤ 6 - 3.75

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x ≥ 2.25/-3

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a(x+b)=4x+10 in the equation above a and b are constants. if the equation has infinitely many solutions for X, what is the value
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Which inverse operation would you use to solve the equation x/6-4=8
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144=12x <br> 45 =4x-27 <br> 2x-2=14 <br> 12x=44-10x does any one kno these questions?
Free_Kalibri [48]

Hello russell6333!

\huge \boxed{\mathfrak{Question} \downarrow}

Solve for x.

  1. 144 = 12x
  2. 45 = 4x - 27
  3. 2x - 2 = 14
  4. 12x = 44 - 10x

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

1) \:  \:  \: 144 = 12x \\  \frac{144}{12}  = x \\ \boxed{ \boxed{  \bf12 = x}}

__________________

2) \:  \:  \: 45 = 4x - 27 \\ 45 + 27 = 4x \\ 72 = 4x \\  \frac{72}{4}  = x \\  \boxed{ \boxed { \bf18 = x }}

__________________

3) \:  \:  \: 2x - 2 = 14 \\ 2x = 14 - 2 \\ 2x = 12 \\ x =  \frac{12}{2}  \\ \boxed{  \boxed{ \bf \: x = 6}}

__________________

4) \:  \:  \: 12x = 44 - 10x \\ 12x + 10x = 44 \\ 22x = 44 \\ x =  \frac{44}{22}  \\  \boxed{\boxed{  \bf \: x = 2}}

__________________

<h3><u>NOTE </u><u>:</u><u>-</u></h3>
  • To solve questions of these sorts, bring all the terms to one side & simplify it leaving x alone in the other side of the equation (other side of the equal to sign). After simplification you'll get the value of x.
  • Remember that the signs & operations will change when you bring a term to the other side of the equation.
  • So, addition will become subtraction, subtraction will become addition, multiplication will become division & division will become multiplication.

__________________

Hope it'll help you!

ℓu¢αzz ッ

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