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Simplifying 169 = 70t + -5t2 Solving 169 = 70t + -5t2 Solving for variable 't'. Reorder the terms: 169 + -70t + 5t2 = 70t + -70t + -5t2 + 5t2 Combine like terms: 70t + -70t = 0 169 + -70t + 5t2 = 0 + -5t2 + 5t2 169 + -70t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 169 + -70t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 33.8 + -14t + t2 = 0 Move the constant term to the right: Add '-33.8' to each side of the equation. 33.8 + -14t + -33.8 + t2 = 0 + -33.8 Reorder the terms: 33.8 + -33.8 + -14t + t2 = 0 + -33.8 Combine like terms: 33.8 + -33.8 = 0.0 0.0 + -14t + t2 = 0 + -33.8 -14t + t2 = 0 + -33.8 Combine like terms: 0 + -33.8 = -33.8 -14t + t2 = -33.8 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 = -33.8 + 49 Reorder the terms: 49 + -14t + t2 = -33.8 + 49 Combine like terms: -33.8 + 49 = 15.2 49 + -14t + t2 = 15.2 Factor a perfect square on the left side: (t + -7)(t + -7) = 15.2 Calculate the square root of the right side: 3.898717738 Break this problem into two subproblems by setting (t + -7) equal to 3.898717738 and -3.898717738.Subproblem 1
t + -7 = 3.898717738 Simplifying t + -7 = 3.898717738 Reorder the terms: -7 + t = 3.898717738 Solving -7 + t = 3.898717738 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 = 3.898717738 + 7 Combine like terms: -7 + 7 = 0 0 + t = 3.898717738 + 7 t = 3.898717738 + 7 Combine like terms: 3.898717738 + 7 = 10.898717738 t = 10.898717738 Simplifying t = 10.898717738Subproblem 2
t + -7 = -3.898717738 Simplifying t + -7 = -3.898717738 Reorder the terms: -7 + t = -3.898717738 Solving -7 + t = -3.898717738 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 = -3.898717738 + 7 Combine like terms: -7 + 7 = 0 0 + t = -3.898717738 + 7 t = -3.898717738 + 7 Combine like terms: -3.898717738 + 7 = 3.101282262 t = 3.101282262 Simplifying t = 3.101282262Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.898717738, 3.101282262}
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