0=-16t^2-64t-12

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Solution for 0=-16t^2-64t-12 equation:


Simplifying
0 = -16t2 + -64t + -12

Reorder the terms:
0 = -12 + -64t + -16t2

Solving
0 = -12 + -64t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 12 = 12
12 + 64t + 16t2 = -12 + -64t + -16t2 + 12 + 64t + 16t2

Reorder the terms:
12 + 64t + 16t2 = -12 + 12 + -64t + 64t + -16t2 + 16t2

Combine like terms: -12 + 12 = 0
12 + 64t + 16t2 = 0 + -64t + 64t + -16t2 + 16t2
12 + 64t + 16t2 = -64t + 64t + -16t2 + 16t2

Combine like terms: -64t + 64t = 0
12 + 64t + 16t2 = 0 + -16t2 + 16t2
12 + 64t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
12 + 64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 16t + 4t2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(3 + 16t + 4t2)' equal to zero and attempt to solve: Simplifying 3 + 16t + 4t2 = 0 Solving 3 + 16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 4t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 4t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 4t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 4t + t2 = 0 + -0.75 4t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 4t + t2 = -0.75 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 = -0.75 + 4 Reorder the terms: 4 + 4t + t2 = -0.75 + 4 Combine like terms: -0.75 + 4 = 3.25 4 + 4t + t2 = 3.25 Factor a perfect square on the left side: (t + 2)(t + 2) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (t + 2) equal to 1.802775638 and -1.802775638.

Subproblem 1

t + 2 = 1.802775638 Simplifying t + 2 = 1.802775638 Reorder the terms: 2 + t = 1.802775638 Solving 2 + t = 1.802775638 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 = 1.802775638 + -2 Combine like terms: 2 + -2 = 0 0 + t = 1.802775638 + -2 t = 1.802775638 + -2 Combine like terms: 1.802775638 + -2 = -0.197224362 t = -0.197224362 Simplifying t = -0.197224362

Subproblem 2

t + 2 = -1.802775638 Simplifying t + 2 = -1.802775638 Reorder the terms: 2 + t = -1.802775638 Solving 2 + t = -1.802775638 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 = -1.802775638 + -2 Combine like terms: 2 + -2 = 0 0 + t = -1.802775638 + -2 t = -1.802775638 + -2 Combine like terms: -1.802775638 + -2 = -3.802775638 t = -3.802775638 Simplifying t = -3.802775638

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.197224362, -3.802775638}

Solution

t = {-0.197224362, -3.802775638}

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