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Simplifying 10t + -0.83t2 = 10 Solving 10t + -0.83t2 = 10 Solving for variable 't'. Reorder the terms: -10 + 10t + -0.83t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 10t + -0.83t2 = 0 Begin completing the square. Divide all terms by -0.83 the coefficient of the squared term: Divide each side by '-0.83'. 12.04819277 + -12.04819277t + t2 = 0 Move the constant term to the right: Add '-12.04819277' to each side of the equation. 12.04819277 + -12.04819277t + -12.04819277 + t2 = 0 + -12.04819277 Reorder the terms: 12.04819277 + -12.04819277 + -12.04819277t + t2 = 0 + -12.04819277 Combine like terms: 12.04819277 + -12.04819277 = 0.00000000 0.00000000 + -12.04819277t + t2 = 0 + -12.04819277 -12.04819277t + t2 = 0 + -12.04819277 Combine like terms: 0 + -12.04819277 = -12.04819277 -12.04819277t + t2 = -12.04819277 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 = -12.04819277 + 36.28973726 Reorder the terms: 36.28973726 + -12.04819277t + t2 = -12.04819277 + 36.28973726 Combine like terms: -12.04819277 + 36.28973726 = 24.24154449 36.28973726 + -12.04819277t + t2 = 24.24154449 Factor a perfect square on the left side: (t + -6.024096385)(t + -6.024096385) = 24.24154449 Calculate the square root of the right side: 4.923570299 Break this problem into two subproblems by setting (t + -6.024096385) equal to 4.923570299 and -4.923570299.Subproblem 1
t + -6.024096385 = 4.923570299 Simplifying t + -6.024096385 = 4.923570299 Reorder the terms: -6.024096385 + t = 4.923570299 Solving -6.024096385 + t = 4.923570299 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 = 4.923570299 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + t = 4.923570299 + 6.024096385 t = 4.923570299 + 6.024096385 Combine like terms: 4.923570299 + 6.024096385 = 10.947666684 t = 10.947666684 Simplifying t = 10.947666684Subproblem 2
t + -6.024096385 = -4.923570299 Simplifying t + -6.024096385 = -4.923570299 Reorder the terms: -6.024096385 + t = -4.923570299 Solving -6.024096385 + t = -4.923570299 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 = -4.923570299 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + t = -4.923570299 + 6.024096385 t = -4.923570299 + 6.024096385 Combine like terms: -4.923570299 + 6.024096385 = 1.100526086 t = 1.100526086 Simplifying t = 1.100526086Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.947666684, 1.100526086}
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