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Simplifying 5(t + -3) * 2t = -30 + -5(4t + -2t) Reorder the terms: 5(-3 + t) * 2t = -30 + -5(4t + -2t) Reorder the terms for easier multiplication: 5 * 2t(-3 + t) = -30 + -5(4t + -2t) Multiply 5 * 2 10t(-3 + t) = -30 + -5(4t + -2t) (-3 * 10t + t * 10t) = -30 + -5(4t + -2t) (-30t + 10t2) = -30 + -5(4t + -2t) Combine like terms: 4t + -2t = 2t -30t + 10t2 = -30 + -5(2t) Remove parenthesis around (2t) -30t + 10t2 = -30 + -5 * 2t Multiply -5 * 2 -30t + 10t2 = -30 + -10t Solving -30t + 10t2 = -30 + -10t Solving for variable 't'. Reorder the terms: 30 + -30t + 10t + 10t2 = -30 + -10t + 30 + 10t Combine like terms: -30t + 10t = -20t 30 + -20t + 10t2 = -30 + -10t + 30 + 10t Reorder the terms: 30 + -20t + 10t2 = -30 + 30 + -10t + 10t Combine like terms: -30 + 30 = 0 30 + -20t + 10t2 = 0 + -10t + 10t 30 + -20t + 10t2 = -10t + 10t Combine like terms: -10t + 10t = 0 30 + -20t + 10t2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(3 + -2t + t2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(3 + -2t + t2)' equal to zero and attempt to solve: Simplifying 3 + -2t + t2 = 0 Solving 3 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -2t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -2t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t + t2 = 0 + -3 -2t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2t + t2 = -3 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 = -3 + 1 Reorder the terms: 1 + -2t + t2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + -2t + t2 = -2 Factor a perfect square on the left side: (t + -1)(t + -1) = -2 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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