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Intercepts of $$$6 x^{2} - 30 \sqrt{2} x + 8 y^{2} - 8 \sqrt{2} y + 67 = 0$$$

The calculator will find the the x- and y-intercepts of $$$6 x^{2} - 30 \sqrt{2} x + 8 y^{2} - 8 \sqrt{2} y + 67 = 0$$$, with steps shown.
Like x+2y=3, y=2x+5 or x^2+3x+4.

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Your Input

Find find the x- and y-intercepts of $$$6 x^{2} - 30 \sqrt{2} x + 8 y^{2} - 8 \sqrt{2} y + 67 = 0$$$.

Solution

To find the x-intercepts, substitute $$$y = 0$$$ into the equation and solve the resulting equation $$$6 x^{2} - 30 \sqrt{2} x + 67 = 0$$$ for $$$x$$$ (use the equation solver).

To find the y-intercepts, substitute $$$x = 0$$$ into the equation and solve the resulting equation $$$8 y^{2} - 8 \sqrt{2} y + 67 = 0$$$ for $$$y$$$ (use the equation solver).

Answer

x-intercepts: $$$\left(\frac{- 4 \sqrt{3} + 15 \sqrt{2}}{6}, 0\right)\approx \left(2.380833367553486, 0\right)$$$, $$$\left(\frac{4 \sqrt{3} + 15 \sqrt{2}}{6}, 0\right)\approx \left(4.690234444311989, 0\right)$$$.

No y-intercepts.

Graph: see the graphing calculator.