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Simplifying 5t + -2(5t + 5) = 23t(54t + 5) Reorder the terms: 5t + -2(5 + 5t) = 23t(54t + 5) 5t + (5 * -2 + 5t * -2) = 23t(54t + 5) 5t + (-10 + -10t) = 23t(54t + 5) Reorder the terms: -10 + 5t + -10t = 23t(54t + 5) Combine like terms: 5t + -10t = -5t -10 + -5t = 23t(54t + 5) Reorder the terms: -10 + -5t = 23t(5 + 54t) -10 + -5t = (5 * 23t + 54t * 23t) -10 + -5t = (115t + 1242t2) Solving -10 + -5t = 115t + 1242t2 Solving for variable 't'. Combine like terms: -5t + -115t = -120t -10 + -120t + -1242t2 = 115t + 1242t2 + -115t + -1242t2 Reorder the terms: -10 + -120t + -1242t2 = 115t + -115t + 1242t2 + -1242t2 Combine like terms: 115t + -115t = 0 -10 + -120t + -1242t2 = 0 + 1242t2 + -1242t2 -10 + -120t + -1242t2 = 1242t2 + -1242t2 Combine like terms: 1242t2 + -1242t2 = 0 -10 + -120t + -1242t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 60t + 621t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 60t + 621t2)' equal to zero and attempt to solve: Simplifying 5 + 60t + 621t2 = 0 Solving 5 + 60t + 621t2 = 0 Begin completing the square. Divide all terms by 621 the coefficient of the squared term: Divide each side by '621'. 0.008051529791 + 0.09661835749t + t2 = 0 Move the constant term to the right: Add '-0.008051529791' to each side of the equation. 0.008051529791 + 0.09661835749t + -0.008051529791 + t2 = 0 + -0.008051529791 Reorder the terms: 0.008051529791 + -0.008051529791 + 0.09661835749t + t2 = 0 + -0.008051529791 Combine like terms: 0.008051529791 + -0.008051529791 = 0.000000000000 0.000000000000 + 0.09661835749t + t2 = 0 + -0.008051529791 0.09661835749t + t2 = 0 + -0.008051529791 Combine like terms: 0 + -0.008051529791 = -0.008051529791 0.09661835749t + t2 = -0.008051529791 The t term is 0.09661835749t. Take half its coefficient (0.04830917875). Square it (0.002333776752) and add it to both sides. Add '0.002333776752' to each side of the equation. 0.09661835749t + 0.002333776752 + t2 = -0.008051529791 + 0.002333776752 Reorder the terms: 0.002333776752 + 0.09661835749t + t2 = -0.008051529791 + 0.002333776752 Combine like terms: -0.008051529791 + 0.002333776752 = -0.005717753039 0.002333776752 + 0.09661835749t + t2 = -0.005717753039 Factor a perfect square on the left side: (t + 0.04830917875)(t + 0.04830917875) = -0.005717753039 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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