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Simplifying 10 = 11t + 9.8t2 Solving 10 = 11t + 9.8t2 Solving for variable 't'. Reorder the terms: 10 + -11t + -9.8t2 = 11t + -11t + 9.8t2 + -9.8t2 Combine like terms: 11t + -11t = 0 10 + -11t + -9.8t2 = 0 + 9.8t2 + -9.8t2 10 + -11t + -9.8t2 = 9.8t2 + -9.8t2 Combine like terms: 9.8t2 + -9.8t2 = 0.0 10 + -11t + -9.8t2 = 0.0 Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -1.020408163 + 1.12244898t + t2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + 1.12244898t + 1.020408163 + t2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + 1.12244898t + t2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + 1.12244898t + t2 = 0 + 1.020408163 1.12244898t + t2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 1.12244898t + t2 = 1.020408163 The t term is 1.12244898t. Take half its coefficient (0.56122449). Square it (0.3149729282) and add it to both sides. Add '0.3149729282' to each side of the equation. 1.12244898t + 0.3149729282 + t2 = 1.020408163 + 0.3149729282 Reorder the terms: 0.3149729282 + 1.12244898t + t2 = 1.020408163 + 0.3149729282 Combine like terms: 1.020408163 + 0.3149729282 = 1.3353810912 0.3149729282 + 1.12244898t + t2 = 1.3353810912 Factor a perfect square on the left side: (t + 0.56122449)(t + 0.56122449) = 1.3353810912 Calculate the square root of the right side: 1.155586903 Break this problem into two subproblems by setting (t + 0.56122449) equal to 1.155586903 and -1.155586903.Subproblem 1
t + 0.56122449 = 1.155586903 Simplifying t + 0.56122449 = 1.155586903 Reorder the terms: 0.56122449 + t = 1.155586903 Solving 0.56122449 + t = 1.155586903 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.56122449' to each side of the equation. 0.56122449 + -0.56122449 + t = 1.155586903 + -0.56122449 Combine like terms: 0.56122449 + -0.56122449 = 0.00000000 0.00000000 + t = 1.155586903 + -0.56122449 t = 1.155586903 + -0.56122449 Combine like terms: 1.155586903 + -0.56122449 = 0.594362413 t = 0.594362413 Simplifying t = 0.594362413Subproblem 2
t + 0.56122449 = -1.155586903 Simplifying t + 0.56122449 = -1.155586903 Reorder the terms: 0.56122449 + t = -1.155586903 Solving 0.56122449 + t = -1.155586903 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.56122449' to each side of the equation. 0.56122449 + -0.56122449 + t = -1.155586903 + -0.56122449 Combine like terms: 0.56122449 + -0.56122449 = 0.00000000 0.00000000 + t = -1.155586903 + -0.56122449 t = -1.155586903 + -0.56122449 Combine like terms: -1.155586903 + -0.56122449 = -1.716811393 t = -1.716811393 Simplifying t = -1.716811393Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.594362413, -1.716811393}
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