0=-16t^2+4t+26

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Solution for 0=-16t^2+4t+26 equation:


Simplifying
0 = -16t2 + 4t + 26

Reorder the terms:
0 = 26 + 4t + -16t2

Solving
0 = 26 + 4t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -26 = -26
-26 + -4t + 16t2 = 26 + 4t + -16t2 + -26 + -4t + 16t2

Reorder the terms:
-26 + -4t + 16t2 = 26 + -26 + 4t + -4t + -16t2 + 16t2

Combine like terms: 26 + -26 = 0
-26 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2
-26 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2

Combine like terms: 4t + -4t = 0
-26 + -4t + 16t2 = 0 + -16t2 + 16t2
-26 + -4t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-26 + -4t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -2t + 8t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-13 + -2t + 8t2)' equal to zero and attempt to solve: Simplifying -13 + -2t + 8t2 = 0 Solving -13 + -2t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + -0.25t + t2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -0.25t + 1.625 + t2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -0.25t + t2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -0.25t + t2 = 0 + 1.625 -0.25t + t2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -0.25t + t2 = 1.625 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = 1.625 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 1.625 + 0.015625 Combine like terms: 1.625 + 0.015625 = 1.640625 0.015625 + -0.25t + t2 = 1.640625 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (t + -0.125) equal to 1.280868846 and -1.280868846.

Subproblem 1

t + -0.125 = 1.280868846 Simplifying t + -0.125 = 1.280868846 Reorder the terms: -0.125 + t = 1.280868846 Solving -0.125 + t = 1.280868846 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 1.280868846 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 1.280868846 + 0.125 t = 1.280868846 + 0.125 Combine like terms: 1.280868846 + 0.125 = 1.405868846 t = 1.405868846 Simplifying t = 1.405868846

Subproblem 2

t + -0.125 = -1.280868846 Simplifying t + -0.125 = -1.280868846 Reorder the terms: -0.125 + t = -1.280868846 Solving -0.125 + t = -1.280868846 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -1.280868846 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -1.280868846 + 0.125 t = -1.280868846 + 0.125 Combine like terms: -1.280868846 + 0.125 = -1.155868846 t = -1.155868846 Simplifying t = -1.155868846

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.405868846, -1.155868846}

Solution

t = {1.405868846, -1.155868846}

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