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Using the quadratic formula to solve x2 = 5 – X, what are the values of X?
-1021
2
-1 + 19
2
5+21
2
1+ /19/
2

Using The Quadratic Formula To Solve X2 5 X What Are The Values Of X 1021 2 1 19 2 521 2 1 19 2 class=

Sagot :

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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