Question

x^2-10x+y^2-20y=-125 what is x+y=?

Answer 1

Complete the square gives you

(x-5)^2+(y-10)^2=0.

Either x-5=0 or y-10=0, so the solutions are x=5 and y=10.

5+10=15, your answer

Answer 2

The value of x + y from the equation $x^2-10x+y^2-20y=-125$ is 15

The equation is given as:

$x^2-10x+y^2-20y=-125$

Add 125 to both sides of the equation

$x^2-10x+y^2-20y+125 = 0$

Express 125 as 100 + 25

$x^2-10x+y^2-20y+100 +25 = 0$

Rewrite the equation as:

$x^2-10x +25+y^2-20y+100 = 0$

Group the expressions

$[x^2-10x +25]+[y^2-20y+100 ]= 0$

Express the expressions in both groups as perfect squares

$(x - 5)^2+(y - 10)^2= 0$

Possible equations from the above equation is:

$(x - 5)^2= 0$ and $(y - 10)^2= 0$

Take the square roots of both sides

$x - 5= 0$ and $y - 10= 0$

Solve for x and y in the above equations

$x = 5$ and $y =10$

So, we have:

$x + y = 5 + 10$

$x + y = 15$

Hence, the value of x + y is 15

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