# I need help with this maths question: Solve by completing the square and write your answers correct to 3 significant figures y^2 - 40y - 3 = 0

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`y^2-40y-3=0`

let we solve it:

`y^2 -(2)(20)+400-403=0 `

`(y-20)^2=403`

`y-20=+-sqrt(403)`

`y=20+-sqrt(403)`

`y_1=40,07485`

`y_2=0,07485`

`y^2-40y-3=0`

To solve using the completing the square method, isolate the constant.

`y^2-40y-3+3=0+3`

`y^2-40y=3`

Then, determine the number that should be added on both sides of the equation. To do so, take half of coefficient of y. And square it.

`y^2-40y+(40/2)^2=3+(40/2)^2`

`y^2-40y+20^2=3+20^2`

`y^2-40y+400=3+400`

`y^2-40y+400=403`

Then, factor left side.

`(y-20)^2=403`

And, isolate y.

`sqrt((y-20)^2)=+-sqrt403`

`y-20=+-sqrt403`

`y-20+20=+-sqrt403+20`

`y=+-sqrt403 + 20`

The `+-` signs before the square root indicates that there are two values of y which are:

`y=sqrt403+20=40.07485989`

`y=-sqrt403+20=-0.07485989987`

**Since the values should be express with three significant figure, then, the solutions to the given equation are y={-0.075, 40.1}.**