Solve (x+0,5)^2=(x-0,7)^2

$$( x + 0,5 ) ^ { 2 } = ( x - 0,7 ) ^ { 2 }$$

Solve for x

$$x=0,1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+0,5\right)^{2}.

$$x^{2}+x+0,25=\left(x-0,7\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-0,7\right)^{2}.

$$x^{2}+x+0,25=x^{2}-1,4x+0,49$$

Subtract x^{2} from both sides.

$$x^{2}+x+0,25-x^{2}=-1,4x+0,49$$

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

$$x+0,25=-1,4x+0,49$$

Add 1,4x to both sides.

$$x+0,25+1,4x=0,49$$

Combine x and 1,4x to get 2,4x.

$$2,4x+0,25=0,49$$

Subtract 0,25 from both sides.

$$2,4x=0,49-0,25$$

Subtract 0,25 from 0,49 to get 0,24.

$$2,4x=0,24$$

Divide both sides by 2,4.

$$x=\frac{0,24}{2,4}$$

Expand \frac{0,24}{2,4} by multiplying both numerator and the denominator by 100.

$$x=\frac{24}{240}$$

Reduce the fraction \frac{24}{240} to lowest terms by extracting and canceling out 24.

$$x=\frac{1}{10}$$