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Simplifying 70 + -10t + -5t2 = 0 Solving 70 + -10t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(14 + -2t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(14 + -2t + -1t2)' equal to zero and attempt to solve: Simplifying 14 + -2t + -1t2 = 0 Solving 14 + -2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 2t + t2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 2t + 14 + t2 = 0 + 14 Reorder the terms: -14 + 14 + 2t + t2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2t + t2 = 0 + 14 2t + t2 = 0 + 14 Combine like terms: 0 + 14 = 14 2t + t2 = 14 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 14 + 1 Reorder the terms: 1 + 2t + t2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + 2t + t2 = 15 Factor a perfect square on the left side: (t + 1)(t + 1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (t + 1) equal to 3.872983346 and -3.872983346.Subproblem 1
t + 1 = 3.872983346 Simplifying t + 1 = 3.872983346 Reorder the terms: 1 + t = 3.872983346 Solving 1 + t = 3.872983346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + t = 3.872983346 + -1 t = 3.872983346 + -1 Combine like terms: 3.872983346 + -1 = 2.872983346 t = 2.872983346 Simplifying t = 2.872983346Subproblem 2
t + 1 = -3.872983346 Simplifying t + 1 = -3.872983346 Reorder the terms: 1 + t = -3.872983346 Solving 1 + t = -3.872983346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + t = -3.872983346 + -1 t = -3.872983346 + -1 Combine like terms: -3.872983346 + -1 = -4.872983346 t = -4.872983346 Simplifying t = -4.872983346Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.872983346, -4.872983346}Solution
t = {2.872983346, -4.872983346}
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