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Simplifying -4.9t2 + 6.4t + 15 = 0 Reorder the terms: 15 + 6.4t + -4.9t2 = 0 Solving 15 + 6.4t + -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'. -3.06122449 + -1.306122449t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -1.306122449t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -1.306122449t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -1.306122449t + t2 = 0 + 3.06122449 -1.306122449t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -1.306122449t + t2 = 3.06122449 The t term is -1.306122449t. Take half its coefficient (-0.6530612245). Square it (0.4264889629) and add it to both sides. Add '0.4264889629' to each side of the equation. -1.306122449t + 0.4264889629 + t2 = 3.06122449 + 0.4264889629 Reorder the terms: 0.4264889629 + -1.306122449t + t2 = 3.06122449 + 0.4264889629 Combine like terms: 3.06122449 + 0.4264889629 = 3.4877134529 0.4264889629 + -1.306122449t + t2 = 3.4877134529 Factor a perfect square on the left side: (t + -0.6530612245)(t + -0.6530612245) = 3.4877134529 Calculate the square root of the right side: 1.867542089 Break this problem into two subproblems by setting (t + -0.6530612245) equal to 1.867542089 and -1.867542089.Subproblem 1
t + -0.6530612245 = 1.867542089 Simplifying t + -0.6530612245 = 1.867542089 Reorder the terms: -0.6530612245 + t = 1.867542089 Solving -0.6530612245 + t = 1.867542089 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6530612245' to each side of the equation. -0.6530612245 + 0.6530612245 + t = 1.867542089 + 0.6530612245 Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000 0.0000000000 + t = 1.867542089 + 0.6530612245 t = 1.867542089 + 0.6530612245 Combine like terms: 1.867542089 + 0.6530612245 = 2.5206033135 t = 2.5206033135 Simplifying t = 2.5206033135Subproblem 2
t + -0.6530612245 = -1.867542089 Simplifying t + -0.6530612245 = -1.867542089 Reorder the terms: -0.6530612245 + t = -1.867542089 Solving -0.6530612245 + t = -1.867542089 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6530612245' to each side of the equation. -0.6530612245 + 0.6530612245 + t = -1.867542089 + 0.6530612245 Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000 0.0000000000 + t = -1.867542089 + 0.6530612245 t = -1.867542089 + 0.6530612245 Combine like terms: -1.867542089 + 0.6530612245 = -1.2144808645 t = -1.2144808645 Simplifying t = -1.2144808645Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.5206033135, -1.2144808645}
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