What is the correct standard form of the equation:
√(x−2)2+(y+5)2
explain each step
what you have is not an equation -- just an expression
Apologies for the confusion. You are correct that what I provided is an expression, not an equation.
In that case, if we want to convert the expression √(x−2)^2+(y+5)^2 into an equation, we set it equal to a constant value. Let's assume that the expression is equal to some constant, say c:
√(x−2)^2+(y+5)^2 = c
This is now an equation with the expression equal to a constant value.
To find the correct standard form of the equation √(x−2)²+(y+5)², we need to simplify it step by step. Here's how:
Step 1: Expand the Square
(x−2)² simplifies to (x−2)(x−2) which equals x²−4x+4.
(y+5)² simplifies to (y+5)(y+5) which equals y²+10y+25.
Step 2: Simplify the Equation
The given equation now becomes:
√(x²−4x+4) + √(y²+10y+25)
Step 3: Combine like terms
Since there are no like terms to combine, we cannot simplify any further.
Therefore, the correct standard form of the equation is:
√(x²−4x+4) + √(y²+10y+25)
To find the correct standard form of the equation, we need to simplify the given expression.
Step 1: Expand the expression
Start by applying the square to both the x and y terms inside the parentheses.
√(x−2)² + (y+5)²
= √(x−2)(x−2) + (y+5)(y+5)
Step 2: Apply algebraic properties
Use the distributive property to multiply both terms inside the parentheses.
= √(x−2)(x−2) + y² + 5y + 5y + 25
Simplify further:
= √(x−2)(x−2) + y² + 10y + 25
Step 3: Simplify under the square root
Since (x−2)(x−2) can be written as (x−2)², we can simplify.
= (x−2)² + y² + 10y + 25
Step 4: Rearrange terms
In standard form, the equation has the x terms first, followed by the y terms with appropriate coefficients.
= (x² - 4x + 4) + y² + 10y + 25
Step 5: Combine like terms
Combine the like terms within the parentheses.
= x² - 4x + 4 + y² + 10y + 25
Step 6: Rearrange terms again
Finally, rearrange the equation in standard form with the x terms first and the constant term last.
= x² - 4x + y² + 10y + 29
Therefore, the correct standard form of the equation is: x² - 4x + y² + 10y + 29
To find the standard form of the equation, we need to simplify the given expression.
Step 1: Expand the square inside the square root:
(x - 2)^2 + (y + 5)^2
Step 2: Simplify the square:
(x - 2)(x - 2) + (y + 5)(y + 5)
Step 3: Apply the FOIL method:
x^2 - 2x - 2x + 4 + y^2 + 5y + 5y + 25
Step 4: Combine like terms:
x^2 - 4x + y^2 + 10y + 29
Therefore, the correct standard form of the equation is:
x^2 - 4x + y^2 + 10y + 29