151t-16t^2=88

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Solution for 151t-16t^2=88 equation:


Simplifying
151t + -16t2 = 88

Solving
151t + -16t2 = 88

Solving for variable 't'.

Reorder the terms:
-88 + 151t + -16t2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + 151t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
5.5 + -9.4375t + t2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -9.4375t + -5.5 + t2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -9.4375t + t2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -9.4375t + t2 = 0 + -5.5
-9.4375t + t2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-9.4375t + t2 = -5.5

The t term is -9.4375t.  Take half its coefficient (-4.71875).
Square it (22.26660156) and add it to both sides.

Add '22.26660156' to each side of the equation.
-9.4375t + 22.26660156 + t2 = -5.5 + 22.26660156

Reorder the terms:
22.26660156 + -9.4375t + t2 = -5.5 + 22.26660156

Combine like terms: -5.5 + 22.26660156 = 16.76660156
22.26660156 + -9.4375t + t2 = 16.76660156

Factor a perfect square on the left side:
(t + -4.71875)(t + -4.71875) = 16.76660156

Calculate the square root of the right side: 4.094704087

Break this problem into two subproblems by setting 
(t + -4.71875) equal to 4.094704087 and -4.094704087.

Subproblem 1

t + -4.71875 = 4.094704087 Simplifying t + -4.71875 = 4.094704087 Reorder the terms: -4.71875 + t = 4.094704087 Solving -4.71875 + t = 4.094704087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.71875' to each side of the equation. -4.71875 + 4.71875 + t = 4.094704087 + 4.71875 Combine like terms: -4.71875 + 4.71875 = 0.00000 0.00000 + t = 4.094704087 + 4.71875 t = 4.094704087 + 4.71875 Combine like terms: 4.094704087 + 4.71875 = 8.813454087 t = 8.813454087 Simplifying t = 8.813454087

Subproblem 2

t + -4.71875 = -4.094704087 Simplifying t + -4.71875 = -4.094704087 Reorder the terms: -4.71875 + t = -4.094704087 Solving -4.71875 + t = -4.094704087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.71875' to each side of the equation. -4.71875 + 4.71875 + t = -4.094704087 + 4.71875 Combine like terms: -4.71875 + 4.71875 = 0.00000 0.00000 + t = -4.094704087 + 4.71875 t = -4.094704087 + 4.71875 Combine like terms: -4.094704087 + 4.71875 = 0.624045913 t = 0.624045913 Simplifying t = 0.624045913

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.813454087, 0.624045913}

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