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Simplifying (-2.7t2) + 35t + 7 = 0 Reorder the terms: 7 + 35t + (-2.7t2) = 0 Solving 7 + 35t + (-2.7t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. -2.592592593 + -12.96296296t + t2 = 0 Move the constant term to the right: Add '2.592592593' to each side of the equation. -2.592592593 + -12.96296296t + 2.592592593 + t2 = 0 + 2.592592593 Reorder the terms: -2.592592593 + 2.592592593 + -12.96296296t + t2 = 0 + 2.592592593 Combine like terms: -2.592592593 + 2.592592593 = 0.000000000 0.000000000 + -12.96296296t + t2 = 0 + 2.592592593 -12.96296296t + t2 = 0 + 2.592592593 Combine like terms: 0 + 2.592592593 = 2.592592593 -12.96296296t + t2 = 2.592592593 The t term is -12.96296296t. Take half its coefficient (-6.48148148). Square it (42.00960218) and add it to both sides. Add '42.00960218' to each side of the equation. -12.96296296t + 42.00960218 + t2 = 2.592592593 + 42.00960218 Reorder the terms: 42.00960218 + -12.96296296t + t2 = 2.592592593 + 42.00960218 Combine like terms: 2.592592593 + 42.00960218 = 44.602194773 42.00960218 + -12.96296296t + t2 = 44.602194773 Factor a perfect square on the left side: ((t) + -6.48148148)((t) + -6.48148148) = 44.602194773 Calculate the square root of the right side: 6.678487461 Break this problem into two subproblems by setting ((t) + -6.48148148) equal to 6.678487461 and -6.678487461.Subproblem 1
(t) + -6.48148148 = 6.678487461 Simplifying (t) + -6.48148148 = 6.678487461 t + -6.48148148 = 6.678487461 Reorder the terms: -6.48148148 + t = 6.678487461 Solving -6.48148148 + t = 6.678487461 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.48148148' to each side of the equation. -6.48148148 + 6.48148148 + t = 6.678487461 + 6.48148148 Combine like terms: -6.48148148 + 6.48148148 = 0.00000000 0.00000000 + t = 6.678487461 + 6.48148148 t = 6.678487461 + 6.48148148 Combine like terms: 6.678487461 + 6.48148148 = 13.159968941 t = 13.159968941 Simplifying t = 13.159968941Subproblem 2
(t) + -6.48148148 = -6.678487461 Simplifying (t) + -6.48148148 = -6.678487461 t + -6.48148148 = -6.678487461 Reorder the terms: -6.48148148 + t = -6.678487461 Solving -6.48148148 + t = -6.678487461 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.48148148' to each side of the equation. -6.48148148 + 6.48148148 + t = -6.678487461 + 6.48148148 Combine like terms: -6.48148148 + 6.48148148 = 0.00000000 0.00000000 + t = -6.678487461 + 6.48148148 t = -6.678487461 + 6.48148148 Combine like terms: -6.678487461 + 6.48148148 = -0.197005981 t = -0.197005981 Simplifying t = -0.197005981Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.159968941, -0.197005981}
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