What are the solutions to the equation solvefor y,x=y^2+8y+19 ?

The solutions to the equation solvefor y,x=y^2+8y+19 are y=-4+sqrt(x-3),y=-sqrt(x-3)-4

Find the zeros of solvefor y,x=y^2+8y+19

The zeros of solvefor y,x=y^2+8y+19 are y=-4+sqrt(x-3),y=-sqrt(x-3)-4

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solve for

y, x = y^{2} + 8 y + 19

y = - 4 + x - 3, y = - x - 3 - 4

Solution steps

x = y^{2} + 8 y + 19

Switch sides

y^{2} + 8 y + 19 = x

Move

x

to the left side

y^{2} + 8 y + 19 - x = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 1 \cdot ( 19 - x )}{2 \cdot 1}

Simplify

8^{2} - 4 \cdot 1 \cdot (19 - x) : 2 x - 3

y_{1, 2} = \frac{- 8 \pm 2 x - 3}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- 8 + 2 x - 3}{2 \cdot 1}, y_{2} = \frac{- 8 - 2 x - 3}{2 \cdot 1}

y = \frac{- 8 + 2 x - 3}{2 \cdot 1} : - 4 + x - 3

y = \frac{- 8 - 2 x - 3}{2 \cdot 1} : - x - 3 - 4

The solutions to the quadratic equation are:

y = - 4 + x - 3, y = - x - 3 - 4

x^{2} \cdot 2 = x + 3

x^{2} - 12 x - 72 = 0

0 = - 16 x^{2} + 177 x + 98

(x^{2} + 5) = 0

x, x^{2} + y^{2} + 10 x + 25 = 0

What are the solutions to the equation solvefor y,x=y^2+8y+19 ?
The solutions to the equation solvefor y,x=y^2+8y+19 are y=-4+sqrt(x-3),y=-sqrt(x-3)-4
Find the zeros of solvefor y,x=y^2+8y+19
The zeros of solvefor y,x=y^2+8y+19 are y=-4+sqrt(x-3),y=-sqrt(x-3)-4