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Simplifying -4.9t2 + 7t + 312 = 0 Reorder the terms: 312 + 7t + -4.9t2 = 0 Solving 312 + 7t + -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'. -63.67346939 + -1.428571429t + t2 = 0 Move the constant term to the right: Add '63.67346939' to each side of the equation. -63.67346939 + -1.428571429t + 63.67346939 + t2 = 0 + 63.67346939 Reorder the terms: -63.67346939 + 63.67346939 + -1.428571429t + t2 = 0 + 63.67346939 Combine like terms: -63.67346939 + 63.67346939 = 0.00000000 0.00000000 + -1.428571429t + t2 = 0 + 63.67346939 -1.428571429t + t2 = 0 + 63.67346939 Combine like terms: 0 + 63.67346939 = 63.67346939 -1.428571429t + t2 = 63.67346939 The t term is -1.428571429t. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429t + 0.5102040819 + t2 = 63.67346939 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429t + t2 = 63.67346939 + 0.5102040819 Combine like terms: 63.67346939 + 0.5102040819 = 64.1836734719 0.5102040819 + -1.428571429t + t2 = 64.1836734719 Factor a perfect square on the left side: (t + -0.7142857145)(t + -0.7142857145) = 64.1836734719 Calculate the square root of the right side: 8.011471367 Break this problem into two subproblems by setting (t + -0.7142857145) equal to 8.011471367 and -8.011471367.Subproblem 1
t + -0.7142857145 = 8.011471367 Simplifying t + -0.7142857145 = 8.011471367 Reorder the terms: -0.7142857145 + t = 8.011471367 Solving -0.7142857145 + t = 8.011471367 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + t = 8.011471367 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = 8.011471367 + 0.7142857145 t = 8.011471367 + 0.7142857145 Combine like terms: 8.011471367 + 0.7142857145 = 8.7257570815 t = 8.7257570815 Simplifying t = 8.7257570815Subproblem 2
t + -0.7142857145 = -8.011471367 Simplifying t + -0.7142857145 = -8.011471367 Reorder the terms: -0.7142857145 + t = -8.011471367 Solving -0.7142857145 + t = -8.011471367 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + t = -8.011471367 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = -8.011471367 + 0.7142857145 t = -8.011471367 + 0.7142857145 Combine like terms: -8.011471367 + 0.7142857145 = -7.2971856525 t = -7.2971856525 Simplifying t = -7.2971856525Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.7257570815, -7.2971856525}
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