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Simplifying 0 = 10t + t2 + 29 Reorder the terms: 0 = 29 + 10t + t2 Solving 0 = 29 + 10t + t2 Solving for variable 't'. Combine like terms: 0 + -29 = -29 -29 + -10t + -1t2 = 29 + 10t + t2 + -29 + -10t + -1t2 Reorder the terms: -29 + -10t + -1t2 = 29 + -29 + 10t + -10t + t2 + -1t2 Combine like terms: 29 + -29 = 0 -29 + -10t + -1t2 = 0 + 10t + -10t + t2 + -1t2 -29 + -10t + -1t2 = 10t + -10t + t2 + -1t2 Combine like terms: 10t + -10t = 0 -29 + -10t + -1t2 = 0 + t2 + -1t2 -29 + -10t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 -29 + -10t + -1t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(29 + 10t + t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(29 + 10t + t2)' equal to zero and attempt to solve: Simplifying 29 + 10t + t2 = 0 Solving 29 + 10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 10t + -29 + t2 = 0 + -29 Reorder the terms: 29 + -29 + 10t + t2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 10t + t2 = 0 + -29 10t + t2 = 0 + -29 Combine like terms: 0 + -29 = -29 10t + t2 = -29 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = -29 + 25 Reorder the terms: 25 + 10t + t2 = -29 + 25 Combine like terms: -29 + 25 = -4 25 + 10t + t2 = -4 Factor a perfect square on the left side: (t + 5)(t + 5) = -4 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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