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Simplifying 7t2 + 28t + -50 = 0 Reorder the terms: -50 + 28t + 7t2 = 0 Solving -50 + 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'. -7.142857143 + 4t + t2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + 4t + 7.142857143 + t2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + 4t + t2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + 4t + t2 = 0 + 7.142857143 4t + t2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 4t + t2 = 7.142857143 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 = 7.142857143 + 4 Reorder the terms: 4 + 4t + t2 = 7.142857143 + 4 Combine like terms: 7.142857143 + 4 = 11.142857143 4 + 4t + t2 = 11.142857143 Factor a perfect square on the left side: (t + 2)(t + 2) = 11.142857143 Calculate the square root of the right side: 3.338091842 Break this problem into two subproblems by setting (t + 2) equal to 3.338091842 and -3.338091842.Subproblem 1
t + 2 = 3.338091842 Simplifying t + 2 = 3.338091842 Reorder the terms: 2 + t = 3.338091842 Solving 2 + t = 3.338091842 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 = 3.338091842 + -2 Combine like terms: 2 + -2 = 0 0 + t = 3.338091842 + -2 t = 3.338091842 + -2 Combine like terms: 3.338091842 + -2 = 1.338091842 t = 1.338091842 Simplifying t = 1.338091842Subproblem 2
t + 2 = -3.338091842 Simplifying t + 2 = -3.338091842 Reorder the terms: 2 + t = -3.338091842 Solving 2 + t = -3.338091842 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 = -3.338091842 + -2 Combine like terms: 2 + -2 = 0 0 + t = -3.338091842 + -2 t = -3.338091842 + -2 Combine like terms: -3.338091842 + -2 = -5.338091842 t = -5.338091842 Simplifying t = -5.338091842Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.338091842, -5.338091842}
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