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Simplifying -1.75t2 + 24.5t + -56.65 = 0 Reorder the terms: -56.65 + 24.5t + -1.75t2 = 0 Solving -56.65 + 24.5t + -1.75t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1.75 the coefficient of the squared term: Divide each side by '-1.75'. 32.37142857 + -14t + t2 = 0 Move the constant term to the right: Add '-32.37142857' to each side of the equation. 32.37142857 + -14t + -32.37142857 + t2 = 0 + -32.37142857 Reorder the terms: 32.37142857 + -32.37142857 + -14t + t2 = 0 + -32.37142857 Combine like terms: 32.37142857 + -32.37142857 = 0.00000000 0.00000000 + -14t + t2 = 0 + -32.37142857 -14t + t2 = 0 + -32.37142857 Combine like terms: 0 + -32.37142857 = -32.37142857 -14t + t2 = -32.37142857 The t term is -14t. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14t + 49 + t2 = -32.37142857 + 49 Reorder the terms: 49 + -14t + t2 = -32.37142857 + 49 Combine like terms: -32.37142857 + 49 = 16.62857143 49 + -14t + t2 = 16.62857143 Factor a perfect square on the left side: (t + -7)(t + -7) = 16.62857143 Calculate the square root of the right side: 4.077814541 Break this problem into two subproblems by setting (t + -7) equal to 4.077814541 and -4.077814541.Subproblem 1
t + -7 = 4.077814541 Simplifying t + -7 = 4.077814541 Reorder the terms: -7 + t = 4.077814541 Solving -7 + t = 4.077814541 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 4.077814541 + 7 Combine like terms: -7 + 7 = 0 0 + t = 4.077814541 + 7 t = 4.077814541 + 7 Combine like terms: 4.077814541 + 7 = 11.077814541 t = 11.077814541 Simplifying t = 11.077814541Subproblem 2
t + -7 = -4.077814541 Simplifying t + -7 = -4.077814541 Reorder the terms: -7 + t = -4.077814541 Solving -7 + t = -4.077814541 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = -4.077814541 + 7 Combine like terms: -7 + 7 = 0 0 + t = -4.077814541 + 7 t = -4.077814541 + 7 Combine like terms: -4.077814541 + 7 = 2.922185459 t = 2.922185459 Simplifying t = 2.922185459Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.077814541, 2.922185459}
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