Answer:
[tex]A)\:x=\frac{-1\pm\sqrt{21}}{2}[/tex]
Step-by-step explanation:
[tex]x^2=5-x[/tex]
Add x from both sides:
[tex]\longmapsto[/tex] [tex]x^2+x=5-x+x[/tex]
[tex]\longmapsto[/tex] [tex]x^2+x=5[/tex]
Subtract 5 from both sides:
[tex]\longmapsto[/tex] [tex]x^2+x-5=5-5[/tex]
[tex]\longmapsto[/tex] [tex]x^2+x-5=0[/tex]
Now, we'll use the quadratic formula to solve this problem: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\longmapsto[/tex] [tex]x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\times \:1\cdot \left(-5\right)}}{2\times \:1}[/tex]
[tex]\longmapsto[/tex] [tex]\sqrt{1^2-4\times \:1\times \left(-5\right)}[/tex]
[tex]\longmapsto[/tex] [tex]1^2=1[/tex]
[tex]\longmapsto[/tex] [tex]\sqrt{1+4\times \:1\times \:5}[/tex]
Multiply 4*1*5= 20
[tex]\longmapsto[/tex] [tex]\sqrt{1+20}[/tex]
Add 1 and 20= 21
[tex]\longmapsto[/tex] [tex]\sqrt{21}[/tex]
[tex]\longmapsto[/tex] [tex]x_{1,\:2}=\frac{-1\pm \sqrt{21}}{2\times \:1}[/tex]
[tex]\longmapsto[/tex] [tex]x_1=\frac{-1+\sqrt{21}}{2\times \:1}[/tex]
[tex]\longmapsto[/tex] [tex]\frac{-1+\sqrt{21}}{2\times \:1}[/tex]
Multiply 2 and 1= 2
[tex]\longmapsto[/tex] [tex]\frac{-1+\sqrt{21}}{2}[/tex]
[tex]\longmapsto[/tex] [tex]x_2=\frac{-1-\sqrt{21}}{2\times \:1}[/tex]
[tex]\longmapsto[/tex] [tex]\frac{-1-\sqrt{21}}{2\times \:1}[/tex]
Multiply 2 and 1= 2
[tex]\longmapsto[/tex] [tex]\frac{-1-\sqrt{21}}{2}[/tex]
[tex]\longmapsto[/tex] [tex]x=\frac{-1+\sqrt{21}}{2},\:x=\frac{-1-\sqrt{21}}{2}[/tex]
[tex]\hookrightarrow[/tex] [tex]x=\frac{-1\pm\sqrt{21}}{2}[/tex]
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