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Simplifying 0 = t2 + 5t + 36 Reorder the terms: 0 = 36 + 5t + t2 Solving 0 = 36 + 5t + t2 Solving for variable 't'. Combine like terms: 0 + -36 = -36 -36 + -5t + -1t2 = 36 + 5t + t2 + -36 + -5t + -1t2 Reorder the terms: -36 + -5t + -1t2 = 36 + -36 + 5t + -5t + t2 + -1t2 Combine like terms: 36 + -36 = 0 -36 + -5t + -1t2 = 0 + 5t + -5t + t2 + -1t2 -36 + -5t + -1t2 = 5t + -5t + t2 + -1t2 Combine like terms: 5t + -5t = 0 -36 + -5t + -1t2 = 0 + t2 + -1t2 -36 + -5t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 -36 + -5t + -1t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(36 + 5t + t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(36 + 5t + t2)' equal to zero and attempt to solve: Simplifying 36 + 5t + t2 = 0 Solving 36 + 5t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 5t + -36 + t2 = 0 + -36 Reorder the terms: 36 + -36 + 5t + t2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 5t + t2 = 0 + -36 5t + t2 = 0 + -36 Combine like terms: 0 + -36 = -36 5t + t2 = -36 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = -36 + 6.25 Reorder the terms: 6.25 + 5t + t2 = -36 + 6.25 Combine like terms: -36 + 6.25 = -29.75 6.25 + 5t + t2 = -29.75 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = -29.75 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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