Mathematics: Convert to standard form 25x^2 + 4y^2 - 50x -75 = 0

Convert to standard form 25x^2 + 4y^2 - 50x -75 - id25242507504418396, ginocousins06

brai9206

14.01.2022

$\frac{(x-1)^{2}}{4}+\frac{y^{2}}{25}=1$

Step-by-step explanation:

we have

$25x^{2}+4y^{2}-50x-75=0$

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$(25x^{2}-50x)+4y^{2}=75$

Factor the leading coefficient of each expression

$25(x^{2}-2x)+4y^{2}=75$

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

$25(x^{2}-2x+1)+4y^{2}=75+25$

$25(x^{2}-2x+1)+4y^{2}=100$

Rewrite as perfect squares

$25(x-1)^{2}+4y^{2}=100$

Divide both sides by the constant term to place the equation in standard form

$\frac{25(x-1)^{2}}{100}+\frac{4y^{2}}{100}=\frac{100}{100}$

Simplify

$\frac{(x-1)^{2}}{4}+\frac{y^{2}}{25}=1$

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johnbobjones

20.09.2021

X = 6

Step-by-step explanation:

Since

$7x = 42 \\ x = \frac{42}{7} \\ x= 6$

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