460=16t^2-4t+472

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Solution for 460=16t^2-4t+472 equation:


Simplifying
460 = 16t2 + -4t + 472

Reorder the terms:
460 = 472 + -4t + 16t2

Solving
460 = 472 + -4t + 16t2

Solving for variable 't'.

Combine like terms: 460 + -472 = -12
-12 + 4t + -16t2 = 472 + -4t + 16t2 + -472 + 4t + -16t2

Reorder the terms:
-12 + 4t + -16t2 = 472 + -472 + -4t + 4t + 16t2 + -16t2

Combine like terms: 472 + -472 = 0
-12 + 4t + -16t2 = 0 + -4t + 4t + 16t2 + -16t2
-12 + 4t + -16t2 = -4t + 4t + 16t2 + -16t2

Combine like terms: -4t + 4t = 0
-12 + 4t + -16t2 = 0 + 16t2 + -16t2
-12 + 4t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-12 + 4t + -16t2 = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + t + -4t2)' equal to zero and attempt to solve: Simplifying -3 + t + -4t2 = 0 Solving -3 + t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.75 + -0.25t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.25t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.25t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.25t + t2 = 0 + -0.75 -0.25t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.25t + t2 = -0.75 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.25t + 0.25 + t2 = -0.75 + 0.25 Reorder the terms: 0.25 + -0.25t + t2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 0.25 + -0.25t + t2 = -0.5 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -0.5 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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