Solve Using the Quadratic Formula 88=151t-16t^2

$88 = 151 t - 16 t^{2}$

Step 1

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

Subtract $151 t$ from both sides of the equation.

$88 - 151 t = - 16 t^{2}$

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

$88 - 151 t + 16 t^{2} = 0$

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 $a = 16$ , $b = - 151$ , and $c = 88$ into the quadratic formula and solve for $t$ .

$\frac{151 \pm \sqrt{{(- 151)}^{2} - 4 \cdot (16 \cdot 88)}}{2 \cdot 16}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 151$ to the power of $2$ .

$t = \frac{151 \pm \sqrt{22801 - 4 \cdot 16 \cdot 88}}{2 \cdot 16}$

Multiply $- 4 \cdot 16 \cdot 88$ .

Multiply $- 4$ by $16$ .

$t = \frac{151 \pm \sqrt{22801 - 64 \cdot 88}}{2 \cdot 16}$

Multiply $- 64$ by $88$ .

$t = \frac{151 \pm \sqrt{22801 - 5632}}{2 \cdot 16}$

Subtract $5632$ from $22801$ .

$t = \frac{151 \pm \sqrt{17169}}{2 \cdot 16}$

Multiply $2$ by $16$ .

$t = \frac{151 \pm \sqrt{17169}}{32}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{151 \pm \sqrt{17169}}{32}$

Decimal Form:

$t = 8.81345408 \dots, 0.62404591 \dots$