Question

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

Answer 1

`A)\:x=(-1\pm√(21))/(2)`

Explanation:

`x^2=5-x`

Add x from both sides:

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

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

Subtract 5 from both sides:

`\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)=(-b\pm √(b^2-4ac))/(2a)`

`\longmapsto`
`x_(1,\:2)=(-1\pm √(1^2-4* \:1\cdot \left(-5\right)))/(2* \:1)`

`\longmapsto`
`√(1^2-4* \:1* \left(-5\right))`

`\longmapsto`
`1^2=1`

`\longmapsto`
`√(1+4* \:1* \:5)`

Multiply 4*1*5= 20

`\longmapsto`
`√(1+20)`

Add 1 and 20= 21

`\longmapsto`
`√(21)`

`\longmapsto`
`x_(1,\:2)=(-1\pm √(21))/(2* \:1)`

`\longmapsto`
`x_1=(-1+√(21))/(2* \:1)`

`\longmapsto`
`(-1+√(21))/(2* \:1)`

Multiply 2 and 1= 2

`\longmapsto`
`(-1+√(21))/(2)`

`\longmapsto`
`x_2=(-1-√(21))/(2* \:1)`

`\longmapsto`
`(-1-√(21))/(2* \:1)`

Multiply 2 and 1= 2

`\longmapsto`
`(-1-√(21))/(2)`

`\longmapsto`
`x=(-1+√(21))/(2),\:x=(-1-√(21))/(2)`

`\hookrightarrow`
`x=(-1\pm√(21))/(2)`

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