Solve (25+t)^2=85^2+(t-12.5)^2

$$( 25 + t ) ^ { 2 } = 85 ^ { 2 } + ( t - 12.5 ) ^ { 2 }$$

Solve for t

$$t = \frac{1081}{12} = 90\frac{1}{12} \approx 90.083333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(25+t\right)^{2}.

$$625+50t+t^{2}=85^{2}+\left(t-12.5\right)^{2}$$

Calculate 85 to the power of 2 and get 7225.

$$625+50t+t^{2}=7225+\left(t-12.5\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(t-12.5\right)^{2}.

$$625+50t+t^{2}=7225+t^{2}-25t+156.25$$

Add 7225 and 156.25 to get 7381.25.

$$625+50t+t^{2}=7381.25+t^{2}-25t$$

Subtract t^{2} from both sides.

$$625+50t+t^{2}-t^{2}=7381.25-25t$$

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

$$625+50t=7381.25-25t$$

Add 25t to both sides.

$$625+50t+25t=7381.25$$

Combine 50t and 25t to get 75t.

$$625+75t=7381.25$$

Subtract 625 from both sides.

$$75t=7381.25-625$$

Subtract 625 from 7381.25 to get 6756.25.

$$75t=6756.25$$

Divide both sides by 75.

$$t=\frac{6756.25}{75}$$

Expand \frac{6756.25}{75} by multiplying both numerator and the denominator by 100.

$$t=\frac{675625}{7500}$$

Reduce the fraction \frac{675625}{7500} to lowest terms by extracting and canceling out 625.

$$t=\frac{1081}{12}$$