Question 1186650
Hello there,
I am currently working on a math problem that I am struggling with.  Please help me solve the following problem:

Use completing the square to write the standard form of the expanded equation

10y^2-8x^2+80x+60y-190=0

___________=1

Thanks so much for your help!

-Diana
<pre>{{{matrix(1,3, 10y^2 - 8x^2 + 80x + 60y - 190, "=", 0)}}}
{{{matrix(2,3, 10y^2 + 60y - 8x^2 + 80x - 190, "=", 0, 10y^2 + 60y - 8x^2 + 80x, "=", 190)}}} ------ Rearranging GIVEN equation, and moving CONSTANT to right-side
{{{matrix(2,3, (10y^2 + 60y) - (8x^2 - 80x), "=", 190, 10(y^2 + 6y) - 8(x^2 - 10x), "=", 190)}}} 
{{{matrix(1,3, 10(y^2 + 6y + ((1/2) * "+ 6")^2) - 8(x^2  -  10x + ((1/2) * - 10)^2), "=", 190 + 10((1/2) * "+ 6")^2 - 8((1/2) * - 10)^2)}}} --- Taking ½ of b on x, also ½ of b on y,                                   
                                                                                                squaring EACH result, then adding to
                                                                                                both sides   
{{{matrix(1,3, 10(y^2 + 6y + ("+ 3")^2) - 8(x^2  -  10x + (- 5)^2), "=", 190 + 10("+ 3")^2 - 8(- 5)^2))}}} 
{{{matrix(1,3, 10(y + 3)^2 - 8(x - 5)^2, "=", 190 + 10(9) - 8(25))}}} 
{{{matrix(1,3, 10(y + 3)^2 - 8(x - 5)^2, "=", 80)}}} 
{{{matrix(1,3, 10(y + 3)^2/80 - 8(x - 5)^2/80, "=", 80/80)}}} ---- Dividing by 80 in order to make right-side, 1
Simplifying entire equation gives us: {{{highlight_green(matrix(1,3, (y + 3)^2/8 - (x - 5)^2/10, "=", 1))}}}</pre>