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

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

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