-16t^2+64t+28=0

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Solution for -16t^2+64t+28=0 equation:


Simplifying
-16t2 + 64t + 28 = 0

Reorder the terms:
28 + 64t + -16t2 = 0

Solving
28 + 64t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 16t + -4t2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(7 + 16t + -4t2)' equal to zero and attempt to solve: Simplifying 7 + 16t + -4t2 = 0 Solving 7 + 16t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -4t + t2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -4t + 1.75 + t2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -4t + t2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -4t + t2 = 0 + 1.75 -4t + t2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -4t + t2 = 1.75 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 = 1.75 + 4 Reorder the terms: 4 + -4t + t2 = 1.75 + 4 Combine like terms: 1.75 + 4 = 5.75 4 + -4t + t2 = 5.75 Factor a perfect square on the left side: (t + -2)(t + -2) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (t + -2) equal to 2.397915762 and -2.397915762.

Subproblem 1

t + -2 = 2.397915762 Simplifying t + -2 = 2.397915762 Reorder the terms: -2 + t = 2.397915762 Solving -2 + t = 2.397915762 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 = 2.397915762 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.397915762 + 2 t = 2.397915762 + 2 Combine like terms: 2.397915762 + 2 = 4.397915762 t = 4.397915762 Simplifying t = 4.397915762

Subproblem 2

t + -2 = -2.397915762 Simplifying t + -2 = -2.397915762 Reorder the terms: -2 + t = -2.397915762 Solving -2 + t = -2.397915762 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 = -2.397915762 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.397915762 + 2 t = -2.397915762 + 2 Combine like terms: -2.397915762 + 2 = -0.397915762 t = -0.397915762 Simplifying t = -0.397915762

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.397915762, -0.397915762}

Solution

t = {4.397915762, -0.397915762}

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