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Simplifying 50 = -5t2 + 10t + 15 Reorder the terms: 50 = 15 + 10t + -5t2 Solving 50 = 15 + 10t + -5t2 Solving for variable 't'. Combine like terms: 50 + -15 = 35 35 + -10t + 5t2 = 15 + 10t + -5t2 + -15 + -10t + 5t2 Reorder the terms: 35 + -10t + 5t2 = 15 + -15 + 10t + -10t + -5t2 + 5t2 Combine like terms: 15 + -15 = 0 35 + -10t + 5t2 = 0 + 10t + -10t + -5t2 + 5t2 35 + -10t + 5t2 = 10t + -10t + -5t2 + 5t2 Combine like terms: 10t + -10t = 0 35 + -10t + 5t2 = 0 + -5t2 + 5t2 35 + -10t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 35 + -10t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(7 + -2t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + -2t + t2)' equal to zero and attempt to solve: Simplifying 7 + -2t + t2 = 0 Solving 7 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -2t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -2t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t + t2 = 0 + -7 -2t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -2t + t2 = -7 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = -7 + 1 Reorder the terms: 1 + -2t + t2 = -7 + 1 Combine like terms: -7 + 1 = -6 1 + -2t + t2 = -6 Factor a perfect square on the left side: (t + -1)(t + -1) = -6 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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