Solve 5left(t+0.33right)^2-5t^2=2.2

$$5 { \left(t+0.33 \right) }^{ 2 } -5 { t }^{ 2 } = 2.2$$

Solve for t

$$t=\frac{301}{600}\approx 0.501666667$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(t+0.33\right)^{2}.

$$5\left(t^{2}+0.66t+0.1089\right)-5t^{2}=2.2$$

Use the distributive property to multiply 5 by t^{2}+0.66t+0.1089.

$$5t^{2}+3.3t+0.5445-5t^{2}=2.2$$

Combine 5t^{2} and -5t^{2} to get 0.

$$3.3t+0.5445=2.2$$

Subtract 0.5445 from both sides.

$$3.3t=2.2-0.5445$$

Subtract 0.5445 from 2.2 to get 1.6555.

$$3.3t=1.6555$$

Divide both sides by 3.3.

$$t=\frac{1.6555}{3.3}$$

Expand \frac{1.6555}{3.3} by multiplying both numerator and the denominator by 10000.

$$t=\frac{16555}{33000}$$

Reduce the fraction \frac{16555}{33000} to lowest terms by extracting and canceling out 55.

$$t=\frac{301}{600}$$