1=5t^2+15t+20

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Solution for 1=5t^2+15t+20 equation:


Simplifying
1 = 5t2 + 15t + 20

Reorder the terms:
1 = 20 + 15t + 5t2

Solving
1 = 20 + 15t + 5t2

Solving for variable 't'.

Combine like terms: 1 + -20 = -19
-19 + -15t + -5t2 = 20 + 15t + 5t2 + -20 + -15t + -5t2

Reorder the terms:
-19 + -15t + -5t2 = 20 + -20 + 15t + -15t + 5t2 + -5t2

Combine like terms: 20 + -20 = 0
-19 + -15t + -5t2 = 0 + 15t + -15t + 5t2 + -5t2
-19 + -15t + -5t2 = 15t + -15t + 5t2 + -5t2

Combine like terms: 15t + -15t = 0
-19 + -15t + -5t2 = 0 + 5t2 + -5t2
-19 + -15t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-19 + -15t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(19 + 15t + 5t2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(19 + 15t + 5t2)' equal to zero and attempt to solve: Simplifying 19 + 15t + 5t2 = 0 Solving 19 + 15t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.8 + 3t + t2 = 0 Move the constant term to the right: Add '-3.8' to each side of the equation. 3.8 + 3t + -3.8 + t2 = 0 + -3.8 Reorder the terms: 3.8 + -3.8 + 3t + t2 = 0 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + 3t + t2 = 0 + -3.8 3t + t2 = 0 + -3.8 Combine like terms: 0 + -3.8 = -3.8 3t + t2 = -3.8 The t term is 3t. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3t + 2.25 + t2 = -3.8 + 2.25 Reorder the terms: 2.25 + 3t + t2 = -3.8 + 2.25 Combine like terms: -3.8 + 2.25 = -1.55 2.25 + 3t + t2 = -1.55 Factor a perfect square on the left side: (t + 1.5)(t + 1.5) = -1.55 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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