Math Problem Statement

y²+4x-14y=-53

Solution

Let's solve the equation y2+4x14y=53y^2 + 4x - 14y = -53.

We are trying to simplify or solve for one of the variables. However, since this is a multivariable equation, it is possible to isolate one variable in terms of the other. Let's express xx in terms of yy.

Steps:

  1. Rearrange the equation: y214y+4x=53y^2 - 14y + 4x = -53
  2. Isolate 4x4x: 4x=53y2+14y4x = -53 - y^2 + 14y
  3. Solve for xx: x=53y2+14y4x = \frac{-53 - y^2 + 14y}{4}

Thus, the solution in terms of xx is: x=53y2+14y4x = \frac{-53 - y^2 + 14y}{4}

Would you like to go over the steps or explore a different approach?

Related Questions:

  1. How would the equation change if we were solving for yy in terms of xx?
  2. What happens if we try completing the square on the y214yy^2 - 14y part?
  3. How does changing the constant value on the right-hand side affect the result?
  4. How can we interpret this equation geometrically?
  5. What if the equation were y2+4x14y=0y^2 + 4x - 14y = 0? How would that affect the solution?

Tip:

When dealing with equations involving multiple variables, isolating one variable can make solving easier and help understand relationships between variables.

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Math Problem Analysis

Mathematical Concepts

Algebra
Multivariable Equations
Rearranging Equations

Formulas

y² - 14y + 4x = -53
x = ( -53 - y² + 14y ) / 4

Theorems

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Suitable Grade Level

Grades 9-11