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Simplifying -5t2 + 8t + 50 = 0 Reorder the terms: 50 + 8t + -5t2 = 0 Solving 50 + 8t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -10 + -1.6t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -1.6t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -1.6t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1.6t + t2 = 0 + 10 -1.6t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1.6t + t2 = 10 The t term is -1.6t. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6t + 0.64 + t2 = 10 + 0.64 Reorder the terms: 0.64 + -1.6t + t2 = 10 + 0.64 Combine like terms: 10 + 0.64 = 10.64 0.64 + -1.6t + t2 = 10.64 Factor a perfect square on the left side: (t + -0.8)(t + -0.8) = 10.64 Calculate the square root of the right side: 3.261901286 Break this problem into two subproblems by setting (t + -0.8) equal to 3.261901286 and -3.261901286.Subproblem 1
t + -0.8 = 3.261901286 Simplifying t + -0.8 = 3.261901286 Reorder the terms: -0.8 + t = 3.261901286 Solving -0.8 + t = 3.261901286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = 3.261901286 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = 3.261901286 + 0.8 t = 3.261901286 + 0.8 Combine like terms: 3.261901286 + 0.8 = 4.061901286 t = 4.061901286 Simplifying t = 4.061901286Subproblem 2
t + -0.8 = -3.261901286 Simplifying t + -0.8 = -3.261901286 Reorder the terms: -0.8 + t = -3.261901286 Solving -0.8 + t = -3.261901286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = -3.261901286 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = -3.261901286 + 0.8 t = -3.261901286 + 0.8 Combine like terms: -3.261901286 + 0.8 = -2.461901286 t = -2.461901286 Simplifying t = -2.461901286Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.061901286, -2.461901286}
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