Solve x^2+(y-3v^2x)2=1

Question

Solve the equation

Solve for x

Solve for v

Solve for y

x = 3 v^{2} + 9 v^{4} + 1 - 2 y x = 3 v^{2} - 9 v^{4} + 1 - 2 y

Evaluate

x^{2} + (y - 3 v^{2} x) \times 2 = 1

Multiply the terms

x^{2} + 2 (y - 3 v^{2} x) = 1

Move the expression to the left side

x^{2} + 2 (y - 3 v^{2} x) - 1 = 0

Calculate

More Steps

x^{2} + 2 y - 6 v^{2} x - 1 = 0

Simplify

x^{2} + 2 y - 1 - 6 v^{2} x = 0

Rewrite in standard form

x^{2} - 6 v^{2} x + 2 y - 1 = 0

Substitute a= 1,b= - 6 v^{2} and c= 2 y - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 v ^{2} \pm ( - 6 v ^{2} ) ^{2} - 4 ( 2 y - 1 )}{2}

Simplify the expression

More Steps

x = \frac{6 v ^{2} \pm 36 v ^{4} - 8 y + 4}{2}

Simplify the radical expression

More Steps

x = \frac{6 v ^{2} \pm 2 9 v ^{4} + 1 - 2 y}{2}

Separate the equation into 2 possible cases

x = \frac{6 v ^{2} + 2 9 v ^{4} + 1 - 2 y}{2} x = \frac{6 v ^{2} - 2 9 v ^{4} + 1 - 2 y}{2}

Simplify the expression

More Steps

x = 3 v^{2} + 9 v^{4} + 1 - 2 y x = \frac{6 v ^{2} - 2 9 v ^{4} + 1 - 2 y}{2}

Solution

More Steps

x = 3 v^{2} + 9 v^{4} + 1 - 2 y x = 3 v^{2} - 9 v^{4} + 1 - 2 y

Show Solution