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Simplifying 210 = -1t2 + 26t + 106 Reorder the terms: 210 = 106 + 26t + -1t2 Solving 210 = 106 + 26t + -1t2 Solving for variable 't'. Combine like terms: 210 + -106 = 104 104 + -26t + t2 = 106 + 26t + -1t2 + -106 + -26t + t2 Reorder the terms: 104 + -26t + t2 = 106 + -106 + 26t + -26t + -1t2 + t2 Combine like terms: 106 + -106 = 0 104 + -26t + t2 = 0 + 26t + -26t + -1t2 + t2 104 + -26t + t2 = 26t + -26t + -1t2 + t2 Combine like terms: 26t + -26t = 0 104 + -26t + t2 = 0 + -1t2 + t2 104 + -26t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 104 + -26t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-104' to each side of the equation. 104 + -26t + -104 + t2 = 0 + -104 Reorder the terms: 104 + -104 + -26t + t2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + -26t + t2 = 0 + -104 -26t + t2 = 0 + -104 Combine like terms: 0 + -104 = -104 -26t + t2 = -104 The t term is -26t. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26t + 169 + t2 = -104 + 169 Reorder the terms: 169 + -26t + t2 = -104 + 169 Combine like terms: -104 + 169 = 65 169 + -26t + t2 = 65 Factor a perfect square on the left side: (t + -13)(t + -13) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (t + -13) equal to 8.062257748 and -8.062257748.Subproblem 1
t + -13 = 8.062257748 Simplifying t + -13 = 8.062257748 Reorder the terms: -13 + t = 8.062257748 Solving -13 + t = 8.062257748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + t = 8.062257748 + 13 Combine like terms: -13 + 13 = 0 0 + t = 8.062257748 + 13 t = 8.062257748 + 13 Combine like terms: 8.062257748 + 13 = 21.062257748 t = 21.062257748 Simplifying t = 21.062257748Subproblem 2
t + -13 = -8.062257748 Simplifying t + -13 = -8.062257748 Reorder the terms: -13 + t = -8.062257748 Solving -13 + t = -8.062257748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + t = -8.062257748 + 13 Combine like terms: -13 + 13 = 0 0 + t = -8.062257748 + 13 t = -8.062257748 + 13 Combine like terms: -8.062257748 + 13 = 4.937742252 t = 4.937742252 Simplifying t = 4.937742252Solution
The solution to the problem is based on the solutions from the subproblems. t = {21.062257748, 4.937742252}
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