4t^2-22t=-34

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Solution for 4t^2-22t=-34 equation:


Simplifying
4t2 + -22t = -34

Reorder the terms:
-22t + 4t2 = -34

Solving
-22t + 4t2 = -34

Solving for variable 't'.

Reorder the terms:
34 + -22t + 4t2 = -34 + 34

Combine like terms: -34 + 34 = 0
34 + -22t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -11t + 2t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(17 + -11t + 2t2)' equal to zero and attempt to solve: Simplifying 17 + -11t + 2t2 = 0 Solving 17 + -11t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -5.5t + t2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -5.5t + -8.5 + t2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -5.5t + t2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -5.5t + t2 = 0 + -8.5 -5.5t + t2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -5.5t + t2 = -8.5 The t term is -5.5t. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t + 7.5625 + t2 = -8.5 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = -8.5 + 7.5625 Combine like terms: -8.5 + 7.5625 = -0.9375 7.5625 + -5.5t + t2 = -0.9375 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = -0.9375 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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