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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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