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Simplifying 112 = -16t2 + 64t Reorder the terms: 112 = 64t + -16t2 Solving 112 = 64t + -16t2 Solving for variable 't'. Reorder the terms: 112 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 112 + -64t + 16t2 = 0 + -16t2 + 16t2 112 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 112 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(7 + -4t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(7 + -4t + t2)' equal to zero and attempt to solve: Simplifying 7 + -4t + t2 = 0 Solving 7 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -4t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -4t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4t + t2 = 0 + -7 -4t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -4t + t2 = -7 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -7 + 4 Reorder the terms: 4 + -4t + t2 = -7 + 4 Combine like terms: -7 + 4 = -3 4 + -4t + t2 = -3 Factor a perfect square on the left side: (t + -2)(t + -2) = -3 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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