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Solve for x x^(2)-6x+y^(2)+2y-15=0

Solve for xx \newlinex2−6x+y2+2y−15=0x^{2}-6x+y^{2}+2y-15=0

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Full solution

Q. Solve for xx \newlinex2−6x+y2+2y−15=0x^{2}-6x+y^{2}+2y-15=0
  1. Rearrange Equation: Step Title: Rearrange the Equation\newlineConcise Step Description: Rearrange the equation to group x and y terms separately.\newlineStep Calculation: x2−6x+y2+2y=15x^2 - 6x + y^2 + 2y = 15\newlineStep Output: x2−6x+y2+2y=15x^2 - 6x + y^2 + 2y = 15
  2. Complete Square for xx: Step Title: Complete the Square for xx Concise Step Description: Complete the square for the xx terms. Step Calculation: x2−6x=(x−3)2−9x^2 - 6x = (x - 3)^2 - 9 Step Output: (x−3)2−9(x - 3)^2 - 9
  3. Complete Square for yy: Step Title: Complete the Square for yy Concise Step Description: Complete the square for the yy terms. Step Calculation: y2+2y=(y+1)2−1y^2 + 2y = (y + 1)^2 - 1 Step Output: (y+1)2−1(y + 1)^2 - 1
  4. Substitute and Simplify: Step Title: Substitute Back and Simplify\newlineConcise Step Description: Substitute the completed squares back into the equation and simplify.\newlineStep Calculation: (x−3)2−9+(y+1)2−1=15(x - 3)^2 - 9 + (y + 1)^2 - 1 = 15\newlineStep Output: (x−3)2+(y+1)2=25(x - 3)^2 + (y + 1)^2 = 25

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