-16t^2+160t+50=0

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Solution for -16t^2+160t+50=0 equation:


Simplifying
-16t2 + 160t + 50 = 0

Reorder the terms:
50 + 160t + -16t2 = 0

Solving
50 + 160t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 80t + -8t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(25 + 80t + -8t2)' equal to zero and attempt to solve: Simplifying 25 + 80t + -8t2 = 0 Solving 25 + 80t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -10t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -10t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -10t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -10t + t2 = 0 + 3.125 -10t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -10t + t2 = 3.125 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 3.125 + 25 Reorder the terms: 25 + -10t + t2 = 3.125 + 25 Combine like terms: 3.125 + 25 = 28.125 25 + -10t + t2 = 28.125 Factor a perfect square on the left side: (t + -5)(t + -5) = 28.125 Calculate the square root of the right side: 5.303300859 Break this problem into two subproblems by setting (t + -5) equal to 5.303300859 and -5.303300859.

Subproblem 1

t + -5 = 5.303300859 Simplifying t + -5 = 5.303300859 Reorder the terms: -5 + t = 5.303300859 Solving -5 + t = 5.303300859 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.303300859 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.303300859 + 5 t = 5.303300859 + 5 Combine like terms: 5.303300859 + 5 = 10.303300859 t = 10.303300859 Simplifying t = 10.303300859

Subproblem 2

t + -5 = -5.303300859 Simplifying t + -5 = -5.303300859 Reorder the terms: -5 + t = -5.303300859 Solving -5 + t = -5.303300859 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.303300859 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.303300859 + 5 t = -5.303300859 + 5 Combine like terms: -5.303300859 + 5 = -0.303300859 t = -0.303300859 Simplifying t = -0.303300859

Solution

The solution to the problem is based on the solutions from the subproblems. t = {10.303300859, -0.303300859}

Solution

t = {10.303300859, -0.303300859}

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