# Solve for t -2t^2+6t+9=0 -2t2+6t+9=0
Factor -1 out of -2t2+6t+9.
Factor -1 out of -2t2.
-(2t2)+6t+9=0
Factor -1 out of 6t.
-(2t2)-(-6t)+9=0
Rewrite 9 as -1(-9).
-(2t2)-(-6t)-1⋅-9=0
Factor -1 out of -(2t2)-(-6t).
-(2t2-6t)-1⋅-9=0
Factor -1 out of -(2t2-6t)-1(-9).
-(2t2-6t-9)=0
-(2t2-6t-9)=0
Multiply each term in -(2t2-6t-9)=0 by -1
Multiply each term in -(2t2-6t-9)=0 by -1.
-(2t2-6t-9)⋅-1=0⋅-1
Simplify -(2t2-6t-9)⋅-1.
Apply the distributive property.
(-(2t2)-(-6t)–9)⋅-1=0⋅-1
Simplify.
Multiply 2 by -1.
(-2t2-(-6t)–9)⋅-1=0⋅-1
Multiply -6 by -1.
(-2t2+6t–9)⋅-1=0⋅-1
Multiply -1 by -9.
(-2t2+6t+9)⋅-1=0⋅-1
(-2t2+6t+9)⋅-1=0⋅-1
Apply the distributive property.
-2t2⋅-1+6t⋅-1+9⋅-1=0⋅-1
Simplify.
Multiply -1 by -2.
2t2+6t⋅-1+9⋅-1=0⋅-1
Multiply -1 by 6.
2t2-6t+9⋅-1=0⋅-1
Multiply 9 by -1.
2t2-6t-9=0⋅-1
2t2-6t-9=0⋅-1
2t2-6t-9=0⋅-1
Multiply 0 by -1.
2t2-6t-9=0
2t2-6t-9=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=2, b=-6, and c=-9 into the quadratic formula and solve for t.
6±(-6)2-4⋅(2⋅-9)2⋅2
Simplify.
Simplify the numerator.
Raise -6 to the power of 2.
t=6±36-4⋅(2⋅-9)2⋅2
Multiply 2 by -9.
t=6±36-4⋅-182⋅2
Multiply -4 by -18.
t=6±36+722⋅2
Add 36 and 72.
t=6±1082⋅2
Rewrite 108 as 62⋅3.
Factor 36 out of 108.
t=6±36(3)2⋅2
Rewrite 36 as 62.
t=6±62⋅32⋅2
t=6±62⋅32⋅2
Pull terms out from under the radical.
t=6±632⋅2
t=6±632⋅2
Multiply 2 by 2.
t=6±634
Simplify 6±634.
t=3±332
t=3±332
The final answer is the combination of both solutions.
t=3+332,3-332
The result can be shown in multiple forms.
Exact Form:
t=3+332,3-332
Decimal Form:
t=4.09807621…,-1.09807621…
Solve for t -2t^2+6t+9=0

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