Basic Math Examples

$0 = - 4.9 {(t - 1.25)}^{2} + 9$

Step 1

Simplify $- 4.9 {(t - 1.25)}^{2} + 9$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(t - 1.25)}^{2}$ as $(t - 1.25) (t - 1.25)$ .

$0 = - 4.9 ((t - 1.25) (t - 1.25)) + 9$

Step 1.1.2

Expand $(t - 1.25) (t - 1.25)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$0 = - 4.9 (t (t - 1.25) - 1.25 (t - 1.25)) + 9$

Step 1.1.2.2

Apply the distributive property.

$0 = - 4.9 (t \cdot t + t \cdot - 1.25 - 1.25 (t - 1.25)) + 9$

Step 1.1.2.3

Apply the distributive property.

$0 = - 4.9 (t \cdot t + t \cdot - 1.25 - 1.25 t - 1.25 \cdot - 1.25) + 9$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $t$ by $t$ .

$0 = - 4.9 (t^{2} + t \cdot - 1.25 - 1.25 t - 1.25 \cdot - 1.25) + 9$

Step 1.1.3.1.2

Move $- 1.25$ to the left of $t$ .

$0 = - 4.9 (t^{2} - 1.25 \cdot t - 1.25 t - 1.25 \cdot - 1.25) + 9$

Step 1.1.3.1.3

Multiply $- 1.25$ by $- 1.25$ .

$0 = - 4.9 (t^{2} - 1.25 t - 1.25 t + 1.5625) + 9$

Step 1.1.3.2

Subtract $1.25 t$ from $- 1.25 t$ .

$0 = - 4.9 (t^{2} - 2.5 t + 1.5625) + 9$

Step 1.1.4

Apply the distributive property.

$0 = - 4.9 t^{2} - 4.9 (- 2.5 t) - 4.9 \cdot 1.5625 + 9$

Step 1.1.5

Simplify.

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Step 1.1.5.1

Multiply $- 2.5$ by $- 4.9$ .

$0 = - 4.9 t^{2} + 12.25 t - 4.9 \cdot 1.5625 + 9$

Step 1.1.5.2

Multiply $- 4.9$ by $1.5625$ .

$0 = - 4.9 t^{2} + 12.25 t - 7.65625 + 9$

Step 1.2

Add $- 7.65625$ and $9$ .

$0 = - 4.9 t^{2} + 12.25 t + 1.34375$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$t \approx - 0.10526185, 2.60526185$

Step 3