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Basic Math
Solve for t 0=-4.9(t-1.25)^2+9
0=-4.9(t-1.25)2+90=−4.9(t−1.25)2+9
Step 1
Simplify -4.9(t-1.25)2+9−4.9(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(t−1.25)2 as (t-1.25)(t-1.25)(t−1.25)(t−1.25).
0=-4.9((t-1.25)(t-1.25))+90=−4.9((t−1.25)(t−1.25))+9
Step 1.1.2
Expand (t-1.25)(t-1.25)(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))+90=−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⋅t+t⋅-1.25-1.25(t-1.25))+90=−4.9(t⋅t+t⋅−1.25−1.25(t−1.25))+9
Step 1.1.2.3
Apply the distributive property.
0=-4.9(t⋅t+t⋅-1.25-1.25t-1.25⋅-1.25)+90=−4.9(t⋅t+t⋅−1.25−1.25t−1.25⋅−1.25)+9
0=-4.9(t⋅t+t⋅-1.25-1.25t-1.25⋅-1.25)+90=−4.9(t⋅t+t⋅−1.25−1.25t−1.25⋅−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 tt by tt.
0=-4.9(t2+t⋅-1.25-1.25t-1.25⋅-1.25)+90=−4.9(t2+t⋅−1.25−1.25t−1.25⋅−1.25)+9
Step 1.1.3.1.2
Move -1.25−1.25 to the left of tt.
0=-4.9(t2-1.25⋅t-1.25t-1.25⋅-1.25)+90=−4.9(t2−1.25⋅t−1.25t−1.25⋅−1.25)+9
Step 1.1.3.1.3
Multiply -1.25 by -1.25.
0=-4.9(t2-1.25t-1.25t+1.5625)+9
0=-4.9(t2-1.25t-1.25t+1.5625)+9
Step 1.1.3.2
Subtract 1.25t from -1.25t.
0=-4.9(t2-2.5t+1.5625)+9
0=-4.9(t2-2.5t+1.5625)+9
Step 1.1.4
Apply the distributive property.
0=-4.9t2-4.9(-2.5t)-4.9⋅1.5625+9
Step 1.1.5
Simplify.
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Step 1.1.5.1
Multiply -2.5 by -4.9.
0=-4.9t2+12.25t-4.9⋅1.5625+9
Step 1.1.5.2
Multiply -4.9 by 1.5625.
0=-4.9t2+12.25t-7.65625+9
0=-4.9t2+12.25t-7.65625+9
0=-4.9t2+12.25t-7.65625+9
Step 1.2
Add -7.65625 and 9.
0=-4.9t2+12.25t+1.34375
0=-4.9t2+12.25t+1.34375
Step 2
Graph each side of the equation. The solution is the x-value of the point of intersection.
t≈-0.10526185,2.60526185
Step 3
 [x2  12  √π  ∫xdx ]