7+20t-16t^2=0

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Solution for 7+20t-16t^2=0 equation:


Simplifying
7 + 20t + -16t2 = 0

Solving
7 + 20t + -16t2 = 0

Solving for variable 't'.

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

Divide each side by '-16'.
-0.4375 + -1.25t + t2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + -1.25t + 0.4375 + t2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + -1.25t + t2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + -1.25t + t2 = 0 + 0.4375
-1.25t + t2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
-1.25t + t2 = 0.4375

The t term is -1.25t.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25t + 0.390625 + t2 = 0.4375 + 0.390625

Reorder the terms:
0.390625 + -1.25t + t2 = 0.4375 + 0.390625

Combine like terms: 0.4375 + 0.390625 = 0.828125
0.390625 + -1.25t + t2 = 0.828125

Factor a perfect square on the left side:
(t + -0.625)(t + -0.625) = 0.828125

Calculate the square root of the right side: 0.910013736

Break this problem into two subproblems by setting 
(t + -0.625) equal to 0.910013736 and -0.910013736.

Subproblem 1

t + -0.625 = 0.910013736 Simplifying t + -0.625 = 0.910013736 Reorder the terms: -0.625 + t = 0.910013736 Solving -0.625 + t = 0.910013736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 0.910013736 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 0.910013736 + 0.625 t = 0.910013736 + 0.625 Combine like terms: 0.910013736 + 0.625 = 1.535013736 t = 1.535013736 Simplifying t = 1.535013736

Subproblem 2

t + -0.625 = -0.910013736 Simplifying t + -0.625 = -0.910013736 Reorder the terms: -0.625 + t = -0.910013736 Solving -0.625 + t = -0.910013736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -0.910013736 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -0.910013736 + 0.625 t = -0.910013736 + 0.625 Combine like terms: -0.910013736 + 0.625 = -0.285013736 t = -0.285013736 Simplifying t = -0.285013736

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.535013736, -0.285013736}

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