Solve -10(t-7)^2+5=1005

$$- 10 ( t - 7 ) ^ { 2 } + 5 = 1005$$

Solve for t

$$t=7-10i$$

$$t=7+10i$$

Steps by Finding Square Root

Subtracting 5 from itself leaves 0.

$$-10\left(t-7\right)^{2}=1005-5$$

Subtract 5 from 1005.

$$-10\left(t-7\right)^{2}=1000$$

Divide both sides by -10.

$$\frac{-10\left(t-7\right)^{2}}{-10}=\frac{1000}{-10}$$

Dividing by -10 undoes the multiplication by -10.

$$\left(t-7\right)^{2}=\frac{1000}{-10}$$

Divide 1000 by -10.

$$\left(t-7\right)^{2}=-100$$

Take the square root of both sides of the equation.

$$t-7=10i t-7=-10i$$

Add 7 to both sides of the equation.

$$t-7-\left(-7\right)=10i-\left(-7\right) t-7-\left(-7\right)=-10i-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$t=10i-\left(-7\right) t=-10i-\left(-7\right)$$

Subtract -7 from 10i.

$$t=7+10i$$

Subtract -7 from -10i.

$$t=7-10i$$

The equation is now solved.

$$t=7+10i t=7-10i$$