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Simplifying -0.83t2 + 10t + 25 = 0 Reorder the terms: 25 + 10t + -0.83t2 = 0 Solving 25 + 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'. -30.12048193 + -12.04819277t + t2 = 0 Move the constant term to the right: Add '30.12048193' to each side of the equation. -30.12048193 + -12.04819277t + 30.12048193 + t2 = 0 + 30.12048193 Reorder the terms: -30.12048193 + 30.12048193 + -12.04819277t + t2 = 0 + 30.12048193 Combine like terms: -30.12048193 + 30.12048193 = 0.00000000 0.00000000 + -12.04819277t + t2 = 0 + 30.12048193 -12.04819277t + t2 = 0 + 30.12048193 Combine like terms: 0 + 30.12048193 = 30.12048193 -12.04819277t + t2 = 30.12048193 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 = 30.12048193 + 36.28973726 Reorder the terms: 36.28973726 + -12.04819277t + t2 = 30.12048193 + 36.28973726 Combine like terms: 30.12048193 + 36.28973726 = 66.41021919 36.28973726 + -12.04819277t + t2 = 66.41021919 Factor a perfect square on the left side: (t + -6.024096385)(t + -6.024096385) = 66.41021919 Calculate the square root of the right side: 8.149246541 Break this problem into two subproblems by setting (t + -6.024096385) equal to 8.149246541 and -8.149246541.Subproblem 1
t + -6.024096385 = 8.149246541 Simplifying t + -6.024096385 = 8.149246541 Reorder the terms: -6.024096385 + t = 8.149246541 Solving -6.024096385 + t = 8.149246541 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 = 8.149246541 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + t = 8.149246541 + 6.024096385 t = 8.149246541 + 6.024096385 Combine like terms: 8.149246541 + 6.024096385 = 14.173342926 t = 14.173342926 Simplifying t = 14.173342926Subproblem 2
t + -6.024096385 = -8.149246541 Simplifying t + -6.024096385 = -8.149246541 Reorder the terms: -6.024096385 + t = -8.149246541 Solving -6.024096385 + t = -8.149246541 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 = -8.149246541 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + t = -8.149246541 + 6.024096385 t = -8.149246541 + 6.024096385 Combine like terms: -8.149246541 + 6.024096385 = -2.125150156 t = -2.125150156 Simplifying t = -2.125150156Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.173342926, -2.125150156}
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