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Simplifying 4.9t2 + 10t + -90 = 0 Reorder the terms: -90 + 10t + 4.9t2 = 0 Solving -90 + 10t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -18.36734694 + 2.040816327t + t2 = 0 Move the constant term to the right: Add '18.36734694' to each side of the equation. -18.36734694 + 2.040816327t + 18.36734694 + t2 = 0 + 18.36734694 Reorder the terms: -18.36734694 + 18.36734694 + 2.040816327t + t2 = 0 + 18.36734694 Combine like terms: -18.36734694 + 18.36734694 = 0.00000000 0.00000000 + 2.040816327t + t2 = 0 + 18.36734694 2.040816327t + t2 = 0 + 18.36734694 Combine like terms: 0 + 18.36734694 = 18.36734694 2.040816327t + t2 = 18.36734694 The t term is 2.040816327t. Take half its coefficient (1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. 2.040816327t + 1.041232821 + t2 = 18.36734694 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327t + t2 = 18.36734694 + 1.041232821 Combine like terms: 18.36734694 + 1.041232821 = 19.408579761 1.041232821 + 2.040816327t + t2 = 19.408579761 Factor a perfect square on the left side: (t + 1.020408164)(t + 1.020408164) = 19.408579761 Calculate the square root of the right side: 4.405516969 Break this problem into two subproblems by setting (t + 1.020408164) equal to 4.405516969 and -4.405516969.Subproblem 1
t + 1.020408164 = 4.405516969 Simplifying t + 1.020408164 = 4.405516969 Reorder the terms: 1.020408164 + t = 4.405516969 Solving 1.020408164 + t = 4.405516969 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + t = 4.405516969 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = 4.405516969 + -1.020408164 t = 4.405516969 + -1.020408164 Combine like terms: 4.405516969 + -1.020408164 = 3.385108805 t = 3.385108805 Simplifying t = 3.385108805Subproblem 2
t + 1.020408164 = -4.405516969 Simplifying t + 1.020408164 = -4.405516969 Reorder the terms: 1.020408164 + t = -4.405516969 Solving 1.020408164 + t = -4.405516969 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + t = -4.405516969 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = -4.405516969 + -1.020408164 t = -4.405516969 + -1.020408164 Combine like terms: -4.405516969 + -1.020408164 = -5.425925133 t = -5.425925133 Simplifying t = -5.425925133Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.385108805, -5.425925133}
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