-16t^2+112t+2=0

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Solution for -16t^2+112t+2=0 equation:


Simplifying
-16t2 + 112t + 2 = 0

Reorder the terms:
2 + 112t + -16t2 = 0

Solving
2 + 112t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 56t + -8t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 56t + -8t2)' equal to zero and attempt to solve: Simplifying 1 + 56t + -8t2 = 0 Solving 1 + 56t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + -7t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -7t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -7t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -7t + t2 = 0 + 0.125 -7t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -7t + t2 = 0.125 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = 0.125 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 0.125 + 12.25 Combine like terms: 0.125 + 12.25 = 12.375 12.25 + -7t + t2 = 12.375 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 12.375 Calculate the square root of the right side: 3.51781182 Break this problem into two subproblems by setting (t + -3.5) equal to 3.51781182 and -3.51781182.

Subproblem 1

t + -3.5 = 3.51781182 Simplifying t + -3.5 = 3.51781182 Reorder the terms: -3.5 + t = 3.51781182 Solving -3.5 + t = 3.51781182 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.51781182 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.51781182 + 3.5 t = 3.51781182 + 3.5 Combine like terms: 3.51781182 + 3.5 = 7.01781182 t = 7.01781182 Simplifying t = 7.01781182

Subproblem 2

t + -3.5 = -3.51781182 Simplifying t + -3.5 = -3.51781182 Reorder the terms: -3.5 + t = -3.51781182 Solving -3.5 + t = -3.51781182 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.51781182 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.51781182 + 3.5 t = -3.51781182 + 3.5 Combine like terms: -3.51781182 + 3.5 = -0.01781182 t = -0.01781182 Simplifying t = -0.01781182

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.01781182, -0.01781182}

Solution

t = {7.01781182, -0.01781182}

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