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Simplifying -2.78t2 + 25t = 30 Reorder the terms: 25t + -2.78t2 = 30 Solving 25t + -2.78t2 = 30 Solving for variable 't'. Reorder the terms: -30 + 25t + -2.78t2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 25t + -2.78t2 = 0 Begin completing the square. Divide all terms by -2.78 the coefficient of the squared term: Divide each side by '-2.78'. 10.79136691 + -8.992805755t + t2 = 0 Move the constant term to the right: Add '-10.79136691' to each side of the equation. 10.79136691 + -8.992805755t + -10.79136691 + t2 = 0 + -10.79136691 Reorder the terms: 10.79136691 + -10.79136691 + -8.992805755t + t2 = 0 + -10.79136691 Combine like terms: 10.79136691 + -10.79136691 = 0.00000000 0.00000000 + -8.992805755t + t2 = 0 + -10.79136691 -8.992805755t + t2 = 0 + -10.79136691 Combine like terms: 0 + -10.79136691 = -10.79136691 -8.992805755t + t2 = -10.79136691 The t term is -8.992805755t. Take half its coefficient (-4.496402878). Square it (20.21763884) and add it to both sides. Add '20.21763884' to each side of the equation. -8.992805755t + 20.21763884 + t2 = -10.79136691 + 20.21763884 Reorder the terms: 20.21763884 + -8.992805755t + t2 = -10.79136691 + 20.21763884 Combine like terms: -10.79136691 + 20.21763884 = 9.42627193 20.21763884 + -8.992805755t + t2 = 9.42627193 Factor a perfect square on the left side: (t + -4.496402878)(t + -4.496402878) = 9.42627193 Calculate the square root of the right side: 3.070223433 Break this problem into two subproblems by setting (t + -4.496402878) equal to 3.070223433 and -3.070223433.Subproblem 1
t + -4.496402878 = 3.070223433 Simplifying t + -4.496402878 = 3.070223433 Reorder the terms: -4.496402878 + t = 3.070223433 Solving -4.496402878 + t = 3.070223433 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.496402878' to each side of the equation. -4.496402878 + 4.496402878 + t = 3.070223433 + 4.496402878 Combine like terms: -4.496402878 + 4.496402878 = 0.000000000 0.000000000 + t = 3.070223433 + 4.496402878 t = 3.070223433 + 4.496402878 Combine like terms: 3.070223433 + 4.496402878 = 7.566626311 t = 7.566626311 Simplifying t = 7.566626311Subproblem 2
t + -4.496402878 = -3.070223433 Simplifying t + -4.496402878 = -3.070223433 Reorder the terms: -4.496402878 + t = -3.070223433 Solving -4.496402878 + t = -3.070223433 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.496402878' to each side of the equation. -4.496402878 + 4.496402878 + t = -3.070223433 + 4.496402878 Combine like terms: -4.496402878 + 4.496402878 = 0.000000000 0.000000000 + t = -3.070223433 + 4.496402878 t = -3.070223433 + 4.496402878 Combine like terms: -3.070223433 + 4.496402878 = 1.426179445 t = 1.426179445 Simplifying t = 1.426179445Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.566626311, 1.426179445}
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