Question

How do you solve using the completing the square method `10x^2 = 4x + 7`?

Answer 1

`x_1=(2+sqrt(74))/10 and x_2=(2-sqrt(74))/10`

Explanation:

`10x^2=4x+7`

`10x^2-4x-7=0`

`100x^2-40x-70=0`

`100x^2-40x+4-74=0`

`(10x-2)^2-(sqrt(74))^2=0`

`(10x-2)^2=(sqrt(74))^2`

Hence `x_1=(2+sqrt(74))/10` and `x_2=(2-sqrt(74))/10`

Answer 2

`x = 1/5 +- sqrt(37/50)`

Explanation:

`10x^2 - 4x = 7`
Divide both sides by 10:
`x^2 - (4x)/10 = 7/10`
`x^2 - (2x/5) = 7/10`
`(x^2 - (2x)/5) + 1/25 = 7/10 + 1/25`
`(x - 1/5)^2 = 37/50`
`(x - 1/5) = +- sqrt(37/50)`
`x = 1/5 +- sqrt(37/50)`