Solve sqrt{2}a^2+7x+5sqrt{2}=0

$$\sqrt { 2 } a ^ { 2 } + 7 x + 5 \sqrt { 2 } = 0$$

Solve for x

$$x=-\frac{\sqrt{2}\left(a^{2}+5\right)}{7}$$

Steps for Solving Linear Equation

Subtract \sqrt{2}a^{2} from both sides. Anything subtracted from zero gives its negation.

$$7x+5\sqrt{2}=-\sqrt{2}a^{2}$$

Subtract 5\sqrt{2} from both sides.

$$7x=-\sqrt{2}a^{2}-5\sqrt{2}$$

Divide both sides by 7.

$$\frac{7x}{7}=-\frac{\sqrt{2}\left(a^{2}+5\right)}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=-\frac{\sqrt{2}\left(a^{2}+5\right)}{7}$$

Solve for a (complex solution)

$$a=-\frac{\sqrt{-14\sqrt{2}x-20}}{2}$$

$$a=\frac{\sqrt{-14\sqrt{2}x-20}}{2}$$

Solve for a

$$a=\frac{\sqrt{-14\sqrt{2}x-20}}{2}$$

$$a=-\frac{\sqrt{-14\sqrt{2}x-20}}{2}\text{, }x\leq -\frac{5\sqrt{2}}{7}$$