Solve -0.7x+(0.5x-3)*(0.5x-3)=0.5x+6.4+(0.5x+1)*(0.5x+1)

$$-0.7x+(0.5x-3) \times (0.5x-3)=0.5x+6.4+(0.5x+1) \times (0.5x+1)$$

Solve for x

$$x=\frac{4}{13}\approx 0.307692308$$

Steps for Solving Linear Equation

Multiply 0.5x-3 and 0.5x-3 to get \left(0.5x-3\right)^{2}.

$$-0.7x+\left(0.5x-3\right)^{2}=0.5x+6.4+\left(0.5x+1\right)\left(0.5x+1\right)$$

Multiply 0.5x+1 and 0.5x+1 to get \left(0.5x+1\right)^{2}.

$$-0.7x+\left(0.5x-3\right)^{2}=0.5x+6.4+\left(0.5x+1\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(0.5x-3\right)^{2}.

$$-0.7x+0.25x^{2}-3x+9=0.5x+6.4+\left(0.5x+1\right)^{2}$$

Combine -0.7x and -3x to get -3.7x.

$$-3.7x+0.25x^{2}+9=0.5x+6.4+\left(0.5x+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(0.5x+1\right)^{2}.

$$-3.7x+0.25x^{2}+9=0.5x+6.4+0.25x^{2}+x+1$$

Combine 0.5x and x to get 1.5x.

$$-3.7x+0.25x^{2}+9=1.5x+6.4+0.25x^{2}+1$$

Add 6.4 and 1 to get 7.4.

$$-3.7x+0.25x^{2}+9=1.5x+7.4+0.25x^{2}$$

Subtract 1.5x from both sides.

$$-3.7x+0.25x^{2}+9-1.5x=7.4+0.25x^{2}$$

Combine -3.7x and -1.5x to get -5.2x.

$$-5.2x+0.25x^{2}+9=7.4+0.25x^{2}$$

Subtract 0.25x^{2} from both sides.

$$-5.2x+0.25x^{2}+9-0.25x^{2}=7.4$$

Combine 0.25x^{2} and -0.25x^{2} to get 0.

$$-5.2x+9=7.4$$

Subtract 9 from both sides.

$$-5.2x=7.4-9$$

Subtract 9 from 7.4 to get -1.6.

$$-5.2x=-1.6$$

Divide both sides by -5.2.

$$x=\frac{-1.6}{-5.2}$$

Expand \frac{-1.6}{-5.2} by multiplying both numerator and the denominator by 10.

$$x=\frac{-16}{-52}$$

Reduce the fraction \frac{-16}{-52} to lowest terms by extracting and canceling out -4.

$$x=\frac{4}{13}$$