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Simplifying 0.83t2 + -10t + 8 = 0 Reorder the terms: 8 + -10t + 0.83t2 = 0 Solving 8 + -10t + 0.83t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.83 the coefficient of the squared term: Divide each side by '0.83'. 9.638554217 + -12.04819277t + t2 = 0 Move the constant term to the right: Add '-9.638554217' to each side of the equation. 9.638554217 + -12.04819277t + -9.638554217 + t2 = 0 + -9.638554217 Reorder the terms: 9.638554217 + -9.638554217 + -12.04819277t + t2 = 0 + -9.638554217 Combine like terms: 9.638554217 + -9.638554217 = 0.000000000 0.000000000 + -12.04819277t + t2 = 0 + -9.638554217 -12.04819277t + t2 = 0 + -9.638554217 Combine like terms: 0 + -9.638554217 = -9.638554217 -12.04819277t + t2 = -9.638554217 The t term is -12.04819277t. Take half its coefficient (-6.024096385). Square it (36.28973726) and add it to both sides. Add '36.28973726' to each side of the equation. -12.04819277t + 36.28973726 + t2 = -9.638554217 + 36.28973726 Reorder the terms: 36.28973726 + -12.04819277t + t2 = -9.638554217 + 36.28973726 Combine like terms: -9.638554217 + 36.28973726 = 26.651183043 36.28973726 + -12.04819277t + t2 = 26.651183043 Factor a perfect square on the left side: (t + -6.024096385)(t + -6.024096385) = 26.651183043 Calculate the square root of the right side: 5.162478382 Break this problem into two subproblems by setting (t + -6.024096385) equal to 5.162478382 and -5.162478382.Subproblem 1
t + -6.024096385 = 5.162478382 Simplifying t + -6.024096385 = 5.162478382 Reorder the terms: -6.024096385 + t = 5.162478382 Solving -6.024096385 + t = 5.162478382 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.024096385' to each side of the equation. -6.024096385 + 6.024096385 + t = 5.162478382 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + t = 5.162478382 + 6.024096385 t = 5.162478382 + 6.024096385 Combine like terms: 5.162478382 + 6.024096385 = 11.186574767 t = 11.186574767 Simplifying t = 11.186574767Subproblem 2
t + -6.024096385 = -5.162478382 Simplifying t + -6.024096385 = -5.162478382 Reorder the terms: -6.024096385 + t = -5.162478382 Solving -6.024096385 + t = -5.162478382 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.024096385' to each side of the equation. -6.024096385 + 6.024096385 + t = -5.162478382 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + t = -5.162478382 + 6.024096385 t = -5.162478382 + 6.024096385 Combine like terms: -5.162478382 + 6.024096385 = 0.861618003 t = 0.861618003 Simplifying t = 0.861618003Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.186574767, 0.861618003}
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