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Simplifying 7t2 + 28t + 8 = 0 Reorder the terms: 8 + 28t + 7t2 = 0 Solving 8 + 28t + 7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.142857143 + 4t + t2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + 4t + -1.142857143 + t2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + 4t + t2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + 4t + t2 = 0 + -1.142857143 4t + t2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 4t + t2 = -1.142857143 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = -1.142857143 + 4 Reorder the terms: 4 + 4t + t2 = -1.142857143 + 4 Combine like terms: -1.142857143 + 4 = 2.857142857 4 + 4t + t2 = 2.857142857 Factor a perfect square on the left side: (t + 2)(t + 2) = 2.857142857 Calculate the square root of the right side: 1.690308509 Break this problem into two subproblems by setting (t + 2) equal to 1.690308509 and -1.690308509.Subproblem 1
t + 2 = 1.690308509 Simplifying t + 2 = 1.690308509 Reorder the terms: 2 + t = 1.690308509 Solving 2 + t = 1.690308509 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 1.690308509 + -2 Combine like terms: 2 + -2 = 0 0 + t = 1.690308509 + -2 t = 1.690308509 + -2 Combine like terms: 1.690308509 + -2 = -0.309691491 t = -0.309691491 Simplifying t = -0.309691491Subproblem 2
t + 2 = -1.690308509 Simplifying t + 2 = -1.690308509 Reorder the terms: 2 + t = -1.690308509 Solving 2 + t = -1.690308509 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -1.690308509 + -2 Combine like terms: 2 + -2 = 0 0 + t = -1.690308509 + -2 t = -1.690308509 + -2 Combine like terms: -1.690308509 + -2 = -3.690308509 t = -3.690308509 Simplifying t = -3.690308509Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.309691491, -3.690308509}
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