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Simplifying 120 = -8t2 + 48t + 40 Reorder the terms: 120 = 40 + 48t + -8t2 Solving 120 = 40 + 48t + -8t2 Solving for variable 't'. Combine like terms: 120 + -40 = 80 80 + -48t + 8t2 = 40 + 48t + -8t2 + -40 + -48t + 8t2 Reorder the terms: 80 + -48t + 8t2 = 40 + -40 + 48t + -48t + -8t2 + 8t2 Combine like terms: 40 + -40 = 0 80 + -48t + 8t2 = 0 + 48t + -48t + -8t2 + 8t2 80 + -48t + 8t2 = 48t + -48t + -8t2 + 8t2 Combine like terms: 48t + -48t = 0 80 + -48t + 8t2 = 0 + -8t2 + 8t2 80 + -48t + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 80 + -48t + 8t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(10 + -6t + t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(10 + -6t + t2)' equal to zero and attempt to solve: Simplifying 10 + -6t + t2 = 0 Solving 10 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -6t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + -6t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -6t + t2 = 0 + -10 -6t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 -6t + t2 = -10 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -10 + 9 Reorder the terms: 9 + -6t + t2 = -10 + 9 Combine like terms: -10 + 9 = -1 9 + -6t + t2 = -1 Factor a perfect square on the left side: (t + -3)(t + -3) = -1 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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