-16t^2+64t+50=0

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Solution for -16t^2+64t+50=0 equation:


Simplifying
-16t2 + 64t + 50 = 0

Reorder the terms:
50 + 64t + -16t2 = 0

Solving
50 + 64t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 32t + -8t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(25 + 32t + -8t2)' equal to zero and attempt to solve: Simplifying 25 + 32t + -8t2 = 0 Solving 25 + 32t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -4t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -4t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -4t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -4t + t2 = 0 + 3.125 -4t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -4t + t2 = 3.125 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 3.125 + 4 Reorder the terms: 4 + -4t + t2 = 3.125 + 4 Combine like terms: 3.125 + 4 = 7.125 4 + -4t + t2 = 7.125 Factor a perfect square on the left side: (t + -2)(t + -2) = 7.125 Calculate the square root of the right side: 2.669269563 Break this problem into two subproblems by setting (t + -2) equal to 2.669269563 and -2.669269563.

Subproblem 1

t + -2 = 2.669269563 Simplifying t + -2 = 2.669269563 Reorder the terms: -2 + t = 2.669269563 Solving -2 + t = 2.669269563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.669269563 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.669269563 + 2 t = 2.669269563 + 2 Combine like terms: 2.669269563 + 2 = 4.669269563 t = 4.669269563 Simplifying t = 4.669269563

Subproblem 2

t + -2 = -2.669269563 Simplifying t + -2 = -2.669269563 Reorder the terms: -2 + t = -2.669269563 Solving -2 + t = -2.669269563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.669269563 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.669269563 + 2 t = -2.669269563 + 2 Combine like terms: -2.669269563 + 2 = -0.669269563 t = -0.669269563 Simplifying t = -0.669269563

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.669269563, -0.669269563}

Solution

t = {4.669269563, -0.669269563}

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