Solve 1+{left(5/8-xright)}^2=1/4+left(1-xright)^2+25/64

$$1+ { \left( \frac{ 5 }{ 8 } -x \right) }^{ 2 } = \frac{ 1 }{ 4 } + { \left(1-x \right) }^{ 2 } + \frac{ 25 }{ 64 }$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{5}{8}-x\right)^{2}.

$$1+\frac{25}{64}-\frac{5}{4}x+x^{2}=\frac{1}{4}+\left(1-x\right)^{2}+\frac{25}{64}$$

Add 1 and \frac{25}{64} to get \frac{89}{64}.

$$\frac{89}{64}-\frac{5}{4}x+x^{2}=\frac{1}{4}+\left(1-x\right)^{2}+\frac{25}{64}$$

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

$$\frac{89}{64}-\frac{5}{4}x+x^{2}=\frac{1}{4}+1-2x+x^{2}+\frac{25}{64}$$

Add \frac{1}{4} and 1 to get \frac{5}{4}.

$$\frac{89}{64}-\frac{5}{4}x+x^{2}=\frac{5}{4}-2x+x^{2}+\frac{25}{64}$$

Add \frac{5}{4} and \frac{25}{64} to get \frac{105}{64}.

$$\frac{89}{64}-\frac{5}{4}x+x^{2}=\frac{105}{64}-2x+x^{2}$$

Add 2x to both sides.

$$\frac{89}{64}-\frac{5}{4}x+x^{2}+2x=\frac{105}{64}+x^{2}$$

Combine -\frac{5}{4}x and 2x to get \frac{3}{4}x.

$$\frac{89}{64}+\frac{3}{4}x+x^{2}=\frac{105}{64}+x^{2}$$

Subtract x^{2} from both sides.

$$\frac{89}{64}+\frac{3}{4}x+x^{2}-x^{2}=\frac{105}{64}$$

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

$$\frac{89}{64}+\frac{3}{4}x=\frac{105}{64}$$

Subtract \frac{89}{64} from both sides.

$$\frac{3}{4}x=\frac{105}{64}-\frac{89}{64}$$

Subtract \frac{89}{64} from \frac{105}{64} to get \frac{1}{4}.

$$\frac{3}{4}x=\frac{1}{4}$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$x=\frac{1}{4}\times \frac{4}{3}$$

Multiply \frac{1}{4} and \frac{4}{3} to get \frac{1}{3}.

$$x=\frac{1}{3}$$