Solve x_1^2-2-(x-0.8)=-2(0.9+x)

$$x _ { 1 } ^ { 2 } - 2 - ( x - 0.8 ) = - 2 ( 0.9 + x )$$

Solve for x

$$x=-\left(x_{1}^{2}+0.6\right)$$

Solution Steps

To find the opposite of x-0.8, find the opposite of each term.

$$x_{1}^{2}-2-x+0.8=-2\left(0.9+x\right)$$

Add -2 and 0.8 to get -1.2.

$$x_{1}^{2}-1.2-x=-2\left(0.9+x\right)$$

Use the distributive property to multiply -2 by 0.9+x.

$$x_{1}^{2}-1.2-x=-1.8-2x$$

Add 2x to both sides.

$$x_{1}^{2}-1.2-x+2x=-1.8$$

Combine -x and 2x to get x.

$$x_{1}^{2}-1.2+x=-1.8$$

Subtract x_{1}^{2} from both sides.

$$-1.2+x=-1.8-x_{1}^{2}$$

Add 1.2 to both sides.

$$x=-1.8-x_{1}^{2}+1.2$$

Add -1.8 and 1.2 to get -0.6.

$$x=-0.6-x_{1}^{2}$$

Solve for x_1 (complex solution)

$$x_{1}=-i\sqrt{x+0.6}$$

$$x_{1}=i\sqrt{x+0.6}$$

Solve for x_1

$$x_{1}=\frac{\sqrt{-4x-2.4}}{2}$$

$$x_{1}=-\frac{\sqrt{-4x-2.4}}{2}\text{, }x\leq -\frac{3}{5}$$