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Simplifying -4.9t2 + 7.87t + -2.4 = 0 Reorder the terms: -2.4 + 7.87t + -4.9t2 = 0 Solving -2.4 + 7.87t + -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'. 0.4897959184 + -1.606122449t + t2 = 0 Move the constant term to the right: Add '-0.4897959184' to each side of the equation. 0.4897959184 + -1.606122449t + -0.4897959184 + t2 = 0 + -0.4897959184 Reorder the terms: 0.4897959184 + -0.4897959184 + -1.606122449t + t2 = 0 + -0.4897959184 Combine like terms: 0.4897959184 + -0.4897959184 = 0.0000000000 0.0000000000 + -1.606122449t + t2 = 0 + -0.4897959184 -1.606122449t + t2 = 0 + -0.4897959184 Combine like terms: 0 + -0.4897959184 = -0.4897959184 -1.606122449t + t2 = -0.4897959184 The t term is -1.606122449t. Take half its coefficient (-0.8030612245). Square it (0.6449073303) and add it to both sides. Add '0.6449073303' to each side of the equation. -1.606122449t + 0.6449073303 + t2 = -0.4897959184 + 0.6449073303 Reorder the terms: 0.6449073303 + -1.606122449t + t2 = -0.4897959184 + 0.6449073303 Combine like terms: -0.4897959184 + 0.6449073303 = 0.1551114119 0.6449073303 + -1.606122449t + t2 = 0.1551114119 Factor a perfect square on the left side: (t + -0.8030612245)(t + -0.8030612245) = 0.1551114119 Calculate the square root of the right side: 0.393841862 Break this problem into two subproblems by setting (t + -0.8030612245) equal to 0.393841862 and -0.393841862.Subproblem 1
t + -0.8030612245 = 0.393841862 Simplifying t + -0.8030612245 = 0.393841862 Reorder the terms: -0.8030612245 + t = 0.393841862 Solving -0.8030612245 + t = 0.393841862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8030612245' to each side of the equation. -0.8030612245 + 0.8030612245 + t = 0.393841862 + 0.8030612245 Combine like terms: -0.8030612245 + 0.8030612245 = 0.0000000000 0.0000000000 + t = 0.393841862 + 0.8030612245 t = 0.393841862 + 0.8030612245 Combine like terms: 0.393841862 + 0.8030612245 = 1.1969030865 t = 1.1969030865 Simplifying t = 1.1969030865Subproblem 2
t + -0.8030612245 = -0.393841862 Simplifying t + -0.8030612245 = -0.393841862 Reorder the terms: -0.8030612245 + t = -0.393841862 Solving -0.8030612245 + t = -0.393841862 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8030612245' to each side of the equation. -0.8030612245 + 0.8030612245 + t = -0.393841862 + 0.8030612245 Combine like terms: -0.8030612245 + 0.8030612245 = 0.0000000000 0.0000000000 + t = -0.393841862 + 0.8030612245 t = -0.393841862 + 0.8030612245 Combine like terms: -0.393841862 + 0.8030612245 = 0.4092193625 t = 0.4092193625 Simplifying t = 0.4092193625Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.1969030865, 0.4092193625}
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