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Simplifying 80 = 90t + -5t2 Solving 80 = 90t + -5t2 Solving for variable 't'. Reorder the terms: 80 + -90t + 5t2 = 90t + -90t + -5t2 + 5t2 Combine like terms: 90t + -90t = 0 80 + -90t + 5t2 = 0 + -5t2 + 5t2 80 + -90t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 80 + -90t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(16 + -18t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(16 + -18t + t2)' equal to zero and attempt to solve: Simplifying 16 + -18t + t2 = 0 Solving 16 + -18t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -18t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + -18t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -18t + t2 = 0 + -16 -18t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 -18t + t2 = -16 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = -16 + 81 Reorder the terms: 81 + -18t + t2 = -16 + 81 Combine like terms: -16 + 81 = 65 81 + -18t + t2 = 65 Factor a perfect square on the left side: (t + -9)(t + -9) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (t + -9) equal to 8.062257748 and -8.062257748.Subproblem 1
t + -9 = 8.062257748 Simplifying t + -9 = 8.062257748 Reorder the terms: -9 + t = 8.062257748 Solving -9 + t = 8.062257748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + t = 8.062257748 + 9 t = 8.062257748 + 9 Combine like terms: 8.062257748 + 9 = 17.062257748 t = 17.062257748 Simplifying t = 17.062257748Subproblem 2
t + -9 = -8.062257748 Simplifying t + -9 = -8.062257748 Reorder the terms: -9 + t = -8.062257748 Solving -9 + t = -8.062257748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + t = -8.062257748 + 9 t = -8.062257748 + 9 Combine like terms: -8.062257748 + 9 = 0.937742252 t = 0.937742252 Simplifying t = 0.937742252Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.062257748, 0.937742252}Solution
t = {17.062257748, 0.937742252}
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