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Simplifying 70 + 34t + -9.8t2 = 0 Solving 70 + 34t + -9.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -7.142857143 + -3.469387755t + t2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + -3.469387755t + 7.142857143 + t2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + -3.469387755t + t2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + -3.469387755t + t2 = 0 + 7.142857143 -3.469387755t + t2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 -3.469387755t + t2 = 7.142857143 The t term is -3.469387755t. Take half its coefficient (-1.734693878). Square it (3.009162850) and add it to both sides. Add '3.009162850' to each side of the equation. -3.469387755t + 3.009162850 + t2 = 7.142857143 + 3.009162850 Reorder the terms: 3.009162850 + -3.469387755t + t2 = 7.142857143 + 3.009162850 Combine like terms: 7.142857143 + 3.009162850 = 10.152019993 3.009162850 + -3.469387755t + t2 = 10.152019993 Factor a perfect square on the left side: (t + -1.734693878)(t + -1.734693878) = 10.152019993 Calculate the square root of the right side: 3.186223469 Break this problem into two subproblems by setting (t + -1.734693878) equal to 3.186223469 and -3.186223469.Subproblem 1
t + -1.734693878 = 3.186223469 Simplifying t + -1.734693878 = 3.186223469 Reorder the terms: -1.734693878 + t = 3.186223469 Solving -1.734693878 + t = 3.186223469 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + t = 3.186223469 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + t = 3.186223469 + 1.734693878 t = 3.186223469 + 1.734693878 Combine like terms: 3.186223469 + 1.734693878 = 4.920917347 t = 4.920917347 Simplifying t = 4.920917347Subproblem 2
t + -1.734693878 = -3.186223469 Simplifying t + -1.734693878 = -3.186223469 Reorder the terms: -1.734693878 + t = -3.186223469 Solving -1.734693878 + t = -3.186223469 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + t = -3.186223469 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + t = -3.186223469 + 1.734693878 t = -3.186223469 + 1.734693878 Combine like terms: -3.186223469 + 1.734693878 = -1.451529591 t = -1.451529591 Simplifying t = -1.451529591Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.920917347, -1.451529591}
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