-4t^2+16t+10=0

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Solution for -4t^2+16t+10=0 equation:


Simplifying
-4t2 + 16t + 10 = 0

Reorder the terms:
10 + 16t + -4t2 = 0

Solving
10 + 16t + -4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 8t + -2t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + 8t + -2t2)' equal to zero and attempt to solve: Simplifying 5 + 8t + -2t2 = 0 Solving 5 + 8t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2.5 + -4t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -4t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -4t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -4t + t2 = 0 + 2.5 -4t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -4t + t2 = 2.5 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 = 2.5 + 4 Reorder the terms: 4 + -4t + t2 = 2.5 + 4 Combine like terms: 2.5 + 4 = 6.5 4 + -4t + t2 = 6.5 Factor a perfect square on the left side: (t + -2)(t + -2) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (t + -2) equal to 2.549509757 and -2.549509757.

Subproblem 1

t + -2 = 2.549509757 Simplifying t + -2 = 2.549509757 Reorder the terms: -2 + t = 2.549509757 Solving -2 + t = 2.549509757 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 = 2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.549509757 + 2 t = 2.549509757 + 2 Combine like terms: 2.549509757 + 2 = 4.549509757 t = 4.549509757 Simplifying t = 4.549509757

Subproblem 2

t + -2 = -2.549509757 Simplifying t + -2 = -2.549509757 Reorder the terms: -2 + t = -2.549509757 Solving -2 + t = -2.549509757 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 = -2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.549509757 + 2 t = -2.549509757 + 2 Combine like terms: -2.549509757 + 2 = -0.549509757 t = -0.549509757 Simplifying t = -0.549509757

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.549509757, -0.549509757}

Solution

t = {4.549509757, -0.549509757}

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