-16t^2+9t+34=0

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Solution for -16t^2+9t+34=0 equation:


Simplifying
-16t2 + 9t + 34 = 0

Reorder the terms:
34 + 9t + -16t2 = 0

Solving
34 + 9t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-2.125 + -0.5625t + t2 = 0

Move the constant term to the right:

Add '2.125' to each side of the equation.
-2.125 + -0.5625t + 2.125 + t2 = 0 + 2.125

Reorder the terms:
-2.125 + 2.125 + -0.5625t + t2 = 0 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + -0.5625t + t2 = 0 + 2.125
-0.5625t + t2 = 0 + 2.125

Combine like terms: 0 + 2.125 = 2.125
-0.5625t + t2 = 2.125

The t term is -0.5625t.  Take half its coefficient (-0.28125).
Square it (0.0791015625) and add it to both sides.

Add '0.0791015625' to each side of the equation.
-0.5625t + 0.0791015625 + t2 = 2.125 + 0.0791015625

Reorder the terms:
0.0791015625 + -0.5625t + t2 = 2.125 + 0.0791015625

Combine like terms: 2.125 + 0.0791015625 = 2.2041015625
0.0791015625 + -0.5625t + t2 = 2.2041015625

Factor a perfect square on the left side:
(t + -0.28125)(t + -0.28125) = 2.2041015625

Calculate the square root of the right side: 1.48462169

Break this problem into two subproblems by setting 
(t + -0.28125) equal to 1.48462169 and -1.48462169.

Subproblem 1

t + -0.28125 = 1.48462169 Simplifying t + -0.28125 = 1.48462169 Reorder the terms: -0.28125 + t = 1.48462169 Solving -0.28125 + t = 1.48462169 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + t = 1.48462169 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + t = 1.48462169 + 0.28125 t = 1.48462169 + 0.28125 Combine like terms: 1.48462169 + 0.28125 = 1.76587169 t = 1.76587169 Simplifying t = 1.76587169

Subproblem 2

t + -0.28125 = -1.48462169 Simplifying t + -0.28125 = -1.48462169 Reorder the terms: -0.28125 + t = -1.48462169 Solving -0.28125 + t = -1.48462169 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + t = -1.48462169 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + t = -1.48462169 + 0.28125 t = -1.48462169 + 0.28125 Combine like terms: -1.48462169 + 0.28125 = -1.20337169 t = -1.20337169 Simplifying t = -1.20337169

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.76587169, -1.20337169}

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