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Simplifying 90 = 50t + 12.5t2 Solving 90 = 50t + 12.5t2 Solving for variable 't'. Reorder the terms: 90 + -50t + -12.5t2 = 50t + -50t + 12.5t2 + -12.5t2 Combine like terms: 50t + -50t = 0 90 + -50t + -12.5t2 = 0 + 12.5t2 + -12.5t2 90 + -50t + -12.5t2 = 12.5t2 + -12.5t2 Combine like terms: 12.5t2 + -12.5t2 = 0.0 90 + -50t + -12.5t2 = 0.0 Begin completing the square. Divide all terms by -12.5 the coefficient of the squared term: Divide each side by '-12.5'. -7.2 + 4t + t2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 4t + 7.2 + t2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 4t + t2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 4t + t2 = 0 + 7.2 4t + t2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 4t + t2 = 7.2 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 = 7.2 + 4 Reorder the terms: 4 + 4t + t2 = 7.2 + 4 Combine like terms: 7.2 + 4 = 11.2 4 + 4t + t2 = 11.2 Factor a perfect square on the left side: (t + 2)(t + 2) = 11.2 Calculate the square root of the right side: 3.346640106 Break this problem into two subproblems by setting (t + 2) equal to 3.346640106 and -3.346640106.Subproblem 1
t + 2 = 3.346640106 Simplifying t + 2 = 3.346640106 Reorder the terms: 2 + t = 3.346640106 Solving 2 + t = 3.346640106 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 = 3.346640106 + -2 Combine like terms: 2 + -2 = 0 0 + t = 3.346640106 + -2 t = 3.346640106 + -2 Combine like terms: 3.346640106 + -2 = 1.346640106 t = 1.346640106 Simplifying t = 1.346640106Subproblem 2
t + 2 = -3.346640106 Simplifying t + 2 = -3.346640106 Reorder the terms: 2 + t = -3.346640106 Solving 2 + t = -3.346640106 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 = -3.346640106 + -2 Combine like terms: 2 + -2 = 0 0 + t = -3.346640106 + -2 t = -3.346640106 + -2 Combine like terms: -3.346640106 + -2 = -5.346640106 t = -5.346640106 Simplifying t = -5.346640106Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.346640106, -5.346640106}
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