Solve Using the Quadratic Formula 85=175t-16t^2

$85 = 175 t - 16 t^{2}$

Step 1

Move all the expressions to the left side of the equation.

Subtract $175 t$ from both sides of the equation.

$85 - 175 t = - 16 t^{2}$

Add $16 t^{2}$ to both sides of the equation.

$85 - 175 t + 16 t^{2} = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 16$ , $b = - 175$ , and $c = 85$ into the quadratic formula and solve for $t$ .

$\frac{175 \pm \sqrt{{(- 175)}^{2} - 4 \cdot (16 \cdot 85)}}{2 \cdot 16}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 175$ to the power of $2$ .

$t = \frac{175 \pm \sqrt{30625 - 4 \cdot 16 \cdot 85}}{2 \cdot 16}$

Multiply $- 4 \cdot 16 \cdot 85$ .

Multiply $- 4$ by $16$ .

$t = \frac{175 \pm \sqrt{30625 - 64 \cdot 85}}{2 \cdot 16}$

Multiply $- 64$ by $85$ .

$t = \frac{175 \pm \sqrt{30625 - 5440}}{2 \cdot 16}$

Subtract $5440$ from $30625$ .

$t = \frac{175 \pm \sqrt{25185}}{2 \cdot 16}$

Multiply $2$ by $16$ .

$t = \frac{175 \pm \sqrt{25185}}{32}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{175 \pm \sqrt{25185}}{32}$

Decimal Form:

$t = 10.42805706 \dots, 0.50944293 \dots$